Obaid Algahtani
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Obaid Algahtani has a total of 31 co-authors. Here are the top co-authors by number of shared publications:
- Erdal Karapınar
Department of Mathematics, Atılım University, İncek, Ankara, Turkey
3 shared publications - Pranay Goswami
School of Liberal Studies, Dr B.R. Ambedkar University Delhi, Delhi 110006, India
3 shared publications - Badr S. Alkahtani
Mathematics Department, College of Science, King Saud University, Riyadh 11989, Saudi Arabia
2 shared publications - Devendra Kumar
Department of Mathematics, University of Rajasthan, Jaipur 302004, Rajasthan, India
2 shared publications - Imtithal Alzughaibi
Department of Mathematics, College of Science, King Saud University, Riyadh, Saudi Arabia
2 shared publications - Jagdev Singh
Indian Institute of Astrophysics
2 shared publications
Latest Publications
- 1 January 2026
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems - S
- Vol. 25, 233-259
On joint profile multifractal formalisms
In this paper, we formulate joint profile formalisms based on statistics of histograms of joint multiscale quantities. These formalisms allow the simultaneous multifractal analysis of several pointwise exponents derived from collections of measures, functions, signals, or images. We first show that joint profiles improve the upper bounds for joint spectra of regularities that can be derived from joint Legendre spectra, and have the advantage to recover non-concave joint spectra. We illustrate these facts for some bivariate scale-lacunary wavelet series. These series are very important in applications since they mimic the typical behavior of sequences of independent random variables better suited to real-world data modeling. We also show the importance of synchronicity. Then, we focus on the setting of joint $ p_i $-wavelet leaders, $ 1 \leq i \leq I $, $ I \in \mathbb{N} $. We prove that the upper bounds are optimal since they become equalities for some multivariate functions. Finally, we prove generic related results in the sense of Baire's categories.- 1 January 2026
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems - S
- Vol. 25, 233-259
On joint profile multifractal formalisms
In this paper, we formulate joint profile formalisms based on statistics of histograms of joint multiscale quantities. These formalisms allow the simultaneous multifractal analysis of several pointwise exponents derived from collections of measures, functions, signals, or images. We first show that joint profiles improve the upper bounds for joint spectra of regularities that can be derived from joint Legendre spectra, and have the advantage to recover non-concave joint spectra. We illustrate these facts for some bivariate scale-lacunary wavelet series. These series are very important in applications since they mimic the typical behavior of sequences of independent random variables better suited to real-world data modeling. We also show the importance of synchronicity. Then, we focus on the setting of joint $ p_i $-wavelet leaders, $ 1 \leq i \leq I $, $ I \in \mathbb{N} $. We prove that the upper bounds are optimal since they become equalities for some multivariate functions. Finally, we prove generic related results in the sense of Baire's categories.- Open Access
- 14 August 2025
- Published by MDPI AG in Mathematics
- Vol. 13 (16) , 2608
Coherent Control of Diabolic Points of a Hermitian Hamiltonian in a Four-Level Atomic System Using Structured Light Fields
A four-level atomic medium is used to manipulate the diabolic points of the Hermitian Hamiltonian using driving fields of structured light. The diabolic points of the fourth, third, and second orders are observed by the real and imaginary parts of the eigenvalues of the Hermitian Hamiltonian. The diabolic points and degeneracy regions are studied with variation in Rabi frequencies, detuning, and topological charges. The structured light has a key impact on diabolic points. By changing the topological charges, the number of diabolic points and the degeneracy regions are changing. The imaginary part of eigenvalues shows fourth-order diabolic points. At topological charge , the real part of eigenvalues does not show higher-order diabolic points. The obtained results of the diabolic point are helpful in the fields of deformation space, entanglement physics, optomechanical systems, and crystal optics.- 14 August 2025
- Published by MDPI AG in Mathematics
- Vol. 13 (16) , 2608
Open AccessCoherent Control of Diabolic Points of a Hermitian Hamiltonian in a Four-Level Atomic System Using Structured Light Fields
A four-level atomic medium is used to manipulate the diabolic points of the Hermitian Hamiltonian using driving fields of structured light. The diabolic points of the fourth, third, and second orders are observed by the real and imaginary parts of the eigenvalues of the Hermitian Hamiltonian. The diabolic points and degeneracy regions are studied with variation in Rabi frequencies, detuning, and topological charges. The structured light has a key impact on diabolic points. By changing the topological charges, the number of diabolic points and the degeneracy regions are changing. The imaginary part of eigenvalues shows fourth-order diabolic points. At topological charge , the real part of eigenvalues does not show higher-order diabolic points. The obtained results of the diabolic point are helpful in the fields of deformation space, entanglement physics, optomechanical systems, and crystal optics. - Open Access
- 18 April 2025
- Published by Springer Nature in Research Square
Artificial Neural Network-Driven Approaches to Improved Forecasting of Disability Care Expenditures in an Aging Kingdom of Saudi Arabia Population
The total number of older persons globally (those aged 60 years and above) was 202 million in 1950; this total multiplied to attain 901 million and is predicted to triple again in 2100. The growth percentage of the elderly population is quickly improving, and the value of their care shall pose a challenging problem in the future. Notably, the number of older persons in the Kingdom of Saudi Arabia (KSA) is fast growing, from 5 percent of the entire population in 2015 to a predicted 20.9% by 2050. The main problem is the KSA's management of the rising problem of age-related Non-Communicable Diseases (NCD). With the escalating dimensions of the population of older persons and increased prevalence of NCD causes of risk, the occurrence of NCDs in KSA will rise, resulting in a proportional increase in the requirement for medical assistance. In this paper, an Artificial Neural Network-Based Approaches for Improved Forecasting of Disability Care Expenditures in an Aging Kingdom of Saudi Arabia Population (ANNFDCE-AKSAP) method is proposed. The main objective of the ANNFDCE-AKSAP method is to create an accurate and scalable forecasting system capable of addressing the Kingdom's evolving disability care needs. Initially, the ANNFDCE-AKSAP technique utilizes a min-max normalization-based data preprocessing model to ensure consistent scaling across variables. Furthermore, the bidirectional variational autoencoder with the self-attention module (BiVAE‐SAM) model forecasts disability care expenses. Finally, the enriched coati osprey algorithm (ECOA)-based hyperparameter selection process is performed to optimize the prediction results of the BiVAE‐SAM method. A wide range of simulations is accomplished to demonstrate the enhanced performance of the ANNFDCE-AKSAP technique, and the results are inspected using several measures. The comparison study of the ANNFDCE-AKSAP technique illustrated the lowest MSE, 0.0128, and MAE, 0.0942, compared to all other methods.
- 18 April 2025
- Published by Springer Nature in Research Square
Open AccessArtificial Neural Network-Driven Approaches to Improved Forecasting of Disability Care Expenditures in an Aging Kingdom of Saudi Arabia Population
The total number of older persons globally (those aged 60 years and above) was 202 million in 1950; this total multiplied to attain 901 million and is predicted to triple again in 2100. The growth percentage of the elderly population is quickly improving, and the value of their care shall pose a challenging problem in the future. Notably, the number of older persons in the Kingdom of Saudi Arabia (KSA) is fast growing, from 5 percent of the entire population in 2015 to a predicted 20.9% by 2050. The main problem is the KSA's management of the rising problem of age-related Non-Communicable Diseases (NCD). With the escalating dimensions of the population of older persons and increased prevalence of NCD causes of risk, the occurrence of NCDs in KSA will rise, resulting in a proportional increase in the requirement for medical assistance. In this paper, an Artificial Neural Network-Based Approaches for Improved Forecasting of Disability Care Expenditures in an Aging Kingdom of Saudi Arabia Population (ANNFDCE-AKSAP) method is proposed. The main objective of the ANNFDCE-AKSAP method is to create an accurate and scalable forecasting system capable of addressing the Kingdom's evolving disability care needs. Initially, the ANNFDCE-AKSAP technique utilizes a min-max normalization-based data preprocessing model to ensure consistent scaling across variables. Furthermore, the bidirectional variational autoencoder with the self-attention module (BiVAE‐SAM) model forecasts disability care expenses. Finally, the enriched coati osprey algorithm (ECOA)-based hyperparameter selection process is performed to optimize the prediction results of the BiVAE‐SAM method. A wide range of simulations is accomplished to demonstrate the enhanced performance of the ANNFDCE-AKSAP technique, and the results are inspected using several measures. The comparison study of the ANNFDCE-AKSAP technique illustrated the lowest MSE, 0.0128, and MAE, 0.0942, compared to all other methods.
- 1 January 2025
- Published by World Scientific Pub Co Pte Ltd in Fractals
- Vol. 33 (06)
AN EFFICIENT COMPUTATIONAL ALGORITHM BASED ON LEGENDRE POLYNOMIALS FOR FRACTIONAL ORDER SUPPLY CHAIN SYSTEM
Applying an approximate numerical technique to a system of coupled nonlinear ordinary differential equations (ODEs) within a supply chain model is particularly valuable due to its relevance to industrial operations. This paper examines and contrasts two algorithms designed to solve a supply chain model incorporating a control variable and time-fractional derivatives. The first method utilizes the Legendre spectral collocation method (LSCM) combined with Caputo fractional derivatives of arbitrary order. This approach transforms the model into a series of algebraic equations. The second method is based on the fundamental principles of fractional calculus and employs the Newton polynomial interpolation (NPI). Both methods are used to generate numerical solutions for the fractional supply chain model. The effectiveness and accuracy of these computational results are evaluated and compared through various figures and tables presented in the paper.
- 1 January 2025
- Published by World Scientific Pub Co Pte Ltd in Fractals
- Vol. 33 (06)
AN EFFICIENT COMPUTATIONAL ALGORITHM BASED ON LEGENDRE POLYNOMIALS FOR FRACTIONAL ORDER SUPPLY CHAIN SYSTEM
Applying an approximate numerical technique to a system of coupled nonlinear ordinary differential equations (ODEs) within a supply chain model is particularly valuable due to its relevance to industrial operations. This paper examines and contrasts two algorithms designed to solve a supply chain model incorporating a control variable and time-fractional derivatives. The first method utilizes the Legendre spectral collocation method (LSCM) combined with Caputo fractional derivatives of arbitrary order. This approach transforms the model into a series of algebraic equations. The second method is based on the fundamental principles of fractional calculus and employs the Newton polynomial interpolation (NPI). Both methods are used to generate numerical solutions for the fractional supply chain model. The effectiveness and accuracy of these computational results are evaluated and compared through various figures and tables presented in the paper.
- Open Access
- 21 March 2024
- Published by MDPI AG in Fractal and Fractional
- Vol. 8 (3) , 178
Investigation of a Spatio-Temporal Fractal Fractional Coupled Hirota System
This article aims to examine the nonlinear excitations in a coupled Hirota system described by the fractal fractional order derivative. By using the Laplace transform with Adomian decomposition (LADM), the numerical solution for the considered system is derived. It has been shown that the suggested technique offers a systematic and effective method to solve complex nonlinear systems. Employing the Banach contraction theorem, it is confirmed that the LADM leads to a convergent solution. The numerical analysis of the solutions demonstrates the confinement of the carrier wave and the presence of confined wave packets. The dispersion nonlinear parameter reduction equally influences the wave amplitude and spatial width. The localized internal oscillations in the solitary waves decreased the wave collapsing effect at comparatively small dispersion. Furthermore, it is also shown that the amplitude of the solitary wave solution increases by reducing the fractal derivative. It is evident that decreasing the order modifies the nature of the solitary wave solutions and marginally decreases the amplitude. The numerical and approximation solutions correspond effectively for specific values of time (t). However, when the fractal or fractional derivative is set to one by increasing time, the wave amplitude increases. The absolute error analysis between the obtained series solutions and the accurate solutions are also presented.- 21 March 2024
- Published by MDPI AG in Fractal and Fractional
- Vol. 8 (3) , 178
Open AccessInvestigation of a Spatio-Temporal Fractal Fractional Coupled Hirota System
This article aims to examine the nonlinear excitations in a coupled Hirota system described by the fractal fractional order derivative. By using the Laplace transform with Adomian decomposition (LADM), the numerical solution for the considered system is derived. It has been shown that the suggested technique offers a systematic and effective method to solve complex nonlinear systems. Employing the Banach contraction theorem, it is confirmed that the LADM leads to a convergent solution. The numerical analysis of the solutions demonstrates the confinement of the carrier wave and the presence of confined wave packets. The dispersion nonlinear parameter reduction equally influences the wave amplitude and spatial width. The localized internal oscillations in the solitary waves decreased the wave collapsing effect at comparatively small dispersion. Furthermore, it is also shown that the amplitude of the solitary wave solution increases by reducing the fractal derivative. It is evident that decreasing the order modifies the nature of the solitary wave solutions and marginally decreases the amplitude. The numerical and approximation solutions correspond effectively for specific values of time (t). However, when the fractal or fractional derivative is set to one by increasing time, the wave amplitude increases. The absolute error analysis between the obtained series solutions and the accurate solutions are also presented. - 1 January 2024
- Published by World Scientific Pub Co Pte Ltd in Fractals
- Vol. 32 (07n08)
A RELIABLE NUMERICAL ALGORITHM FOR TREATMENT OF FRACTIONAL MODEL OF CONVECTIVE STRAIGHT FINS WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY
Fins serve the purpose of enhancing heat transfer between their surroundings and the underlying surface, resembling the function of heat exchangers in various scientific domains. This research undertakes an investigation into the temperature distribution within convective straight fins, considering the impact of both constant and thermally conductive temperature-dependent properties. The chosen approach utilizes a numerical technique known as the Laguerre operational matrix collocation method, which relies on the Laguerre operational matrix and Laguerre collocation method for Caputo fractional derivatives of arbitrary orders. This methodology effectively converts the issue into a set of nonlinear algebraic equations (NLAEs). To evaluate this arbitrary order model, we employed the collocation method to obtain an approximate solution. The numerical results obtained through this approach demonstrate its ease of application and computational efficiency. In addition, we performed a comparative analysis with the Homotopy Perturbation Sumudu Transform Method (HPSTM) and the Variational Iteration Method (VIM). The numerical and graphical presentation of the results underscores the efficacy and precision of the methodologies employed within the scope of this investigation.
- 1 January 2024
- Published by World Scientific Pub Co Pte Ltd in Fractals
- Vol. 32 (07n08)
A RELIABLE NUMERICAL ALGORITHM FOR TREATMENT OF FRACTIONAL MODEL OF CONVECTIVE STRAIGHT FINS WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY
Fins serve the purpose of enhancing heat transfer between their surroundings and the underlying surface, resembling the function of heat exchangers in various scientific domains. This research undertakes an investigation into the temperature distribution within convective straight fins, considering the impact of both constant and thermally conductive temperature-dependent properties. The chosen approach utilizes a numerical technique known as the Laguerre operational matrix collocation method, which relies on the Laguerre operational matrix and Laguerre collocation method for Caputo fractional derivatives of arbitrary orders. This methodology effectively converts the issue into a set of nonlinear algebraic equations (NLAEs). To evaluate this arbitrary order model, we employed the collocation method to obtain an approximate solution. The numerical results obtained through this approach demonstrate its ease of application and computational efficiency. In addition, we performed a comparative analysis with the Homotopy Perturbation Sumudu Transform Method (HPSTM) and the Variational Iteration Method (VIM). The numerical and graphical presentation of the results underscores the efficacy and precision of the methodologies employed within the scope of this investigation.
- Open Access
- 13 November 2023
- Published by MDPI AG in Fractal and Fractional
- Vol. 7 (11) , 819
On Mixed Fractional Lifting Oscillation Spaces
We introduce hyperbolic oscillation spaces and mixed fractional lifting oscillation spaces expressed in terms of hyperbolic wavelet leaders of multivariate signals on , with . Contrary to Besov spaces and fractional Sobolev spaces with dominating mixed smoothness, the new spaces take into account the geometric disposition of the hyperbolic wavelet coefficients at each scale , and are therefore suitable for a multifractal analysis of rectangular regularity. We prove that hyperbolic oscillation spaces are closely related to hyperbolic variation spaces, and consequently do not almost depend on the chosen hyperbolic wavelet basis. Therefore, the so-called rectangular multifractal analysis, related to hyperbolic oscillation spaces, is somehow ‘robust’, i.e., does not change if the analyzing wavelets were changed. We also study optimal relationships between hyperbolic and mixed fractional lifting oscillation spaces and Besov spaces with dominating mixed smoothness. In particular, we show that, for some indices, hyperbolic and mixed fractional lifting oscillation spaces are not always sharply imbedded between Besov spaces or fractional Sobolev spaces with dominating mixed smoothness, and thus are new spaces of a really different nature.- 13 November 2023
- Published by MDPI AG in Fractal and Fractional
- Vol. 7 (11) , 819
Open AccessOn Mixed Fractional Lifting Oscillation Spaces
We introduce hyperbolic oscillation spaces and mixed fractional lifting oscillation spaces expressed in terms of hyperbolic wavelet leaders of multivariate signals on , with . Contrary to Besov spaces and fractional Sobolev spaces with dominating mixed smoothness, the new spaces take into account the geometric disposition of the hyperbolic wavelet coefficients at each scale , and are therefore suitable for a multifractal analysis of rectangular regularity. We prove that hyperbolic oscillation spaces are closely related to hyperbolic variation spaces, and consequently do not almost depend on the chosen hyperbolic wavelet basis. Therefore, the so-called rectangular multifractal analysis, related to hyperbolic oscillation spaces, is somehow ‘robust’, i.e., does not change if the analyzing wavelets were changed. We also study optimal relationships between hyperbolic and mixed fractional lifting oscillation spaces and Besov spaces with dominating mixed smoothness. In particular, we show that, for some indices, hyperbolic and mixed fractional lifting oscillation spaces are not always sharply imbedded between Besov spaces or fractional Sobolev spaces with dominating mixed smoothness, and thus are new spaces of a really different nature. - Open Access
- 1 January 2023
- Published by Walter de Gruyter GmbH in Nonlinear Engineering
- Vol. 12 (1)
Theoretical and numerical analysis of nonlinear Boussinesq equation under fractal fractional derivative
A nonlinear Boussinesq equation under fractal fractional Caputo’s derivative is studied. The general series solution is calculated using the double Laplace transform with decomposition. The convergence and stability analyses of the model are investigated under Caputo’s fractal fractional derivative. For the numerical illustrations of the obtained solution, specific examples along with suitable initial conditions are considered. The single solitary wave solutions under fractal fractional derivative are attained by considering small values of time . The wave propagation has a symmetrical form. The solitary wave’s amplitude diminishes over time, and its extended tail expands over a long distance. It is observed that the fractal fractional derivatives are an extremely constructive tool for studying nonlinear systems. An error analysis is also carried out for compactness.- 1 January 2023
- Published by Walter de Gruyter GmbH in Nonlinear Engineering
- Vol. 12 (1)
Open AccessTheoretical and numerical analysis of nonlinear Boussinesq equation under fractal fractional derivative
A nonlinear Boussinesq equation under fractal fractional Caputo’s derivative is studied. The general series solution is calculated using the double Laplace transform with decomposition. The convergence and stability analyses of the model are investigated under Caputo’s fractal fractional derivative. For the numerical illustrations of the obtained solution, specific examples along with suitable initial conditions are considered. The single solitary wave solutions under fractal fractional derivative are attained by considering small values of time . The wave propagation has a symmetrical form. The solitary wave’s amplitude diminishes over time, and its extended tail expands over a long distance. It is observed that the fractal fractional derivatives are an extremely constructive tool for studying nonlinear systems. An error analysis is also carried out for compactness. - Open Access
Ulam Stability of Fractional Hybrid Sequential Integro-Differential Equations with Existence and Uniqueness Theory
In this paper, a variety of boundary value problems (BVPs) known as hybrid fractional sequential integro-differential equations (HFSIDs) with two point orders () are investigated. The uniqueness and existence of the solution are discussed via Banach fixed-point theorems. Certain particular theorems associated with Hyers–Ulam and Hyers–Ulam–Rassias stability to the solution, as well as the uniqueness and existence of the solution of the BVPs are studied. The results are illustrated with some particular examples, and the numerical data are analyzed for confirmation of the results. The results obtained in this work are simple and can easily be applicable to physical systems. Furthermore, symmetry analysis of fractional differential equations and HFSIDs are also presented. This is due to the fact that the aforementioned analysis plays a significant role in both the optimization and qualitative theory of fractional differential equations.Open AccessUlam Stability of Fractional Hybrid Sequential Integro-Differential Equations with Existence and Uniqueness Theory
In this paper, a variety of boundary value problems (BVPs) known as hybrid fractional sequential integro-differential equations (HFSIDs) with two point orders () are investigated. The uniqueness and existence of the solution are discussed via Banach fixed-point theorems. Certain particular theorems associated with Hyers–Ulam and Hyers–Ulam–Rassias stability to the solution, as well as the uniqueness and existence of the solution of the BVPs are studied. The results are illustrated with some particular examples, and the numerical data are analyzed for confirmation of the results. The results obtained in this work are simple and can easily be applicable to physical systems. Furthermore, symmetry analysis of fractional differential equations and HFSIDs are also presented. This is due to the fact that the aforementioned analysis plays a significant role in both the optimization and qualitative theory of fractional differential equations. - Open Access
- 1 January 2022
- Published by American Institute of Mathematical Sciences (AIMS) in AIMS Mathematics
- Vol. 7 (9) , 16760-16774
Semi-analytical and numerical study of fractal fractional nonlinear system under Caputo fractional derivative
The article aims to investigate the fractional Drinfeld-Sokolov-Wilson system with fractal dimensions under the power-law kernel. The integral transform with the Adomian decomposition technique is applied to investigate the general series solution as well as study the applications of the considered model with fractal-fractional dimensions. For validity, a numerical case with appropriate subsidiary conditions is considered with a detailed numerical/physical interpretation. The absolute error in the considered exact and obtained series solutions is also presented. From the obtained results, it is revealed that minimizing the fractal dimension reinforces the amplitude of the solitary wave solution. Moreover, one can see that reducing the fractional order $ \alpha $ marginally reduces the amplitude as well as alters the nature of the solitonic waves. It is also revealed that for insignificant values of time, solutions of the coupled system in the form of solitary waves are in good agreement. However, when one of the parameters (fractal/fractional) is one and time increases, the amplitude of the system also increases. From the error analysis, it is noted that the absolute error in the solutions reduces rapidly when $ x $ enlarges at small-time $ t $, whereas, increment in iterations decreases error in the system. Finally, the results show that the considered method is a significant mathematical approach for studying linear/nonlinear FPDE's and therefore can be extensively applied to other physical models.- 1 January 2022
- Published by American Institute of Mathematical Sciences (AIMS) in AIMS Mathematics
- Vol. 7 (9) , 16760-16774
Open AccessSemi-analytical and numerical study of fractal fractional nonlinear system under Caputo fractional derivative
The article aims to investigate the fractional Drinfeld-Sokolov-Wilson system with fractal dimensions under the power-law kernel. The integral transform with the Adomian decomposition technique is applied to investigate the general series solution as well as study the applications of the considered model with fractal-fractional dimensions. For validity, a numerical case with appropriate subsidiary conditions is considered with a detailed numerical/physical interpretation. The absolute error in the considered exact and obtained series solutions is also presented. From the obtained results, it is revealed that minimizing the fractal dimension reinforces the amplitude of the solitary wave solution. Moreover, one can see that reducing the fractional order $ \alpha $ marginally reduces the amplitude as well as alters the nature of the solitonic waves. It is also revealed that for insignificant values of time, solutions of the coupled system in the form of solitary waves are in good agreement. However, when one of the parameters (fractal/fractional) is one and time increases, the amplitude of the system also increases. From the error analysis, it is noted that the absolute error in the solutions reduces rapidly when $ x $ enlarges at small-time $ t $, whereas, increment in iterations decreases error in the system. Finally, the results show that the considered method is a significant mathematical approach for studying linear/nonlinear FPDE's and therefore can be extensively applied to other physical models.