NANura Alotaibi

Nura Alotaibi

Jouf University
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Nura Alotaibi has a total of 11 co-authors. Here are the top co-authors by number of shared publications:

Latest Publications

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    Analytical Solutions for Direct and Inverse Source Problems in a Time-Fractional Diffusion Equation

    by Ghaziyah Alsahli, Nura Alotaibi, Sid Ahmed Ould Beinane, Asim Ilyas

    This investigation is concerned with a time-fractional diffusion equation governed by the Hilfer fractional derivative of order 1<ρ1<2, subject to homogeneous Neumann boundary data and generalized initial conditions of the Hilfer type. This paper addresses three interconnected problems: a direct problem and two inverse source problems (ISPs). In the first ISP, the objective is to recover an unknown space-dependent source function from measurements taken at a specified final time. In the second ISP, the goal is to determine an unknown time-dependent coefficient through an integral-type over-specification condition. By employing eigenfunction expansions in conjunction with the LT technique, we derive explicit series representations of the solutions in terms of the Mittag-Leffler function. Rigorous existence and uniqueness results for classical solutions are established for all three problems. The second ISP is reformulated as a Volterra integral equation, whose unique solvability is demonstrated via the Banach fixed point theorem. Both ISPs are shown to be ill-posed in the Hadamard sense, indicating instability with respect to data perturbations. Numerical experiments are also presented to validate the theoretical findings and to illustrate the performance of the proposed reconstruction methods. As limiting cases, the formulations corresponding to the Riemann–Liouville and Caputo fractional derivatives are recovered, illustrating the generality of the proposed framework.

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    Applying Iterated Function Systems in Waste Recycling Processes by Identifying Fractal-like Patterns in Material Decomposition

    by Ghaziyah Alsahli, Muhammad Nazam, Nura Alotaibi

    This manuscript aims at the introduction of interpolative FG-contractions and their application to derive fixed-point results. As an application, one of the obtained results is used to analyze the fractional-order Aizawa model. Moreover, we introduce a Hutchinson–Barnsley operator defined in terms of interpolative FG-contractions and a related iterated function system to prove the existence of a unique fractal. The theoretical findings are supported with illustrative examples and graphical demonstrations. This manuscript also sheds light on a theoretical framework for analyzing material decomposition and recycling processes.

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    Extending Polynomially Normal Operators to (P, Q)-Normal Operators in Semi-Hilbertian Spaces

    by Sid Ahmed Ould Ahmed Mahmoud, Nura Alotaibi, Sid Ahmed Ould Beinane, Salman Saud Alsaeed

    This paper is devoted to the introduction and systematic study of (P,Q)-normal operators in the context of semi-Hilbertian spaces, where P and Q are non-constant complex polynomials in one variable. This class generalizes the well-known notion of polynomially normal operators and offers a natural setting to study their structural properties in spaces endowed with a semi-inner product induced by a positive operator. We establish fundamental properties of (P,Q)-normal operators, including conditions for commutativity with respect to the A-adjoint and relations to other classes of A-operators. Several examples are provided to illustrate the theory and demonstrate how (P,Q)-normality extends classical concepts in operator theory.

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    On Jordan $ \sigma $-centralizers and related linear maps in algebras

    by Nura Alotaibi

    Let $ \mathcal{B} $ be an algebra over a commutative ring with identity $ S $, and let $ \sigma $: $ \mathcal{B}\to\mathcal{B} $ be an algebra homomorphism. In this paper, we study linear operators $ \Delta $: $ \mathcal{B}\to\mathcal{B} $ that are constrained by zero-product conditions involving the Jordan product $ u\circ v = uv + vu $. In particular, we consider mappings that satisfy $ uv = 0 \Rightarrow \Delta(u\circ v) = \Delta(u)\circ \sigma(v), \; \; \; uv = 0 \Rightarrow \Delta(u\circ v) = \sigma(u)\circ \Delta(v), $ and $ uv = 0 \Rightarrow \Delta(u\circ v) = \Delta(u)\circ\sigma(v) = \sigma(u)\circ\Delta(v). $ Assuming the endomorphism $ \sigma $ is bijective, we prove that the scenario essentially simplifies to the identity case $ \sigma = \mathrm{id}_{\mathcal{B}} $. Such a simplification enables a comprehensive the forms of these linear operators. As a result, we obtain precise expressions for these operators across diverse algebraic structures, including generalized matrix algebras, upper-triangular algebras, von Neumann algebras, standard operator algebras, and nest algebras. Moreover, this approach produces analogous results for Jordan $ \sigma $-centralizers, thus extending and integrating various prior findings in the field.

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    Reconstruction of the Initial Data and Source Functions for a Wave Equation with Nonlocal Boundary Condition

    by Sid Ahmed Ould Beinane, Nura Alotaibi, Ghaziyah Alsahli, Asim Ilyas

    This paper addresses multiple inverse source problems linked to the wave equation under nonlocal boundary conditions. A bi-orthogonal functional framework is adopted to represent the solutions through series expansions. The analysis establishes that these problems are ill-posed in the Hadamard sense. Three main reconstruction tasks are considered: identification of an unknown space-dependent source, recovery of the initial data, and estimation of a time-varying source term. For each case, suitable additional conditions are introduced to ensure the uniqueness of the unknown quantities. Existence and uniqueness theorems are proved under specific smoothness requirements. Finally, the theoretical developments are validated through numerical computations.

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    A Structural Study of Generalized [m,C]-Symmetric Extension Operators

    by Sid Ould Ahmed Mahmoud, El Moctar Ould Beiba, Sid Ahmed Ould Beinane, Nura Alotaibi

    This manuscript introduces and investigates a new class of operators, termedn-quasi-[m,C]-symmetric operators, which generalize and extend the existing notions of [m,C]-symmetric and n-quasi-[m,C]-isometric operators. Specifically, given a conjugation C on a Hilbert space, an operator Q∈B(K) is said to be n-quasi-[m,C]-symmetric if it satisfies the relationQ∗n∑0≤j≤m(−1)jmjCQm−jCQjQn=0. Our study systematically explores the algebraic properties and structural characterization of n-quasi-[m,C]-symmetric operators through matrix representations, providing a deeper understanding of their internal structure. Moreover, we establish sufficient conditions under which the powers and products of such operators inherit the n-quasi-[m,C]-symmetric property. Additionally, we investigate the tensor products of n-quasi-[m,C]-symmetric operators. Finally, we identify conditions that distinguish n-quasi-[m,C]-symmetric operators from n-quasi-[m−1;C]-symmetric operators.

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    Mathematical Modelling and Optimal Control Technique and Analysis of Insecticides Susceptibility in Status on Mosquitoes and Community Knowledge on Malaria

    by Ghaziyah Alsahli, Adamu Gambo, Nura Alotaibi

    This study focuses on developing a mathematical model to analyse the effects of insecticide application on mosquito populations and the role of community awareness in controlling malaria transmission. The model incorporates factors such as insecticide resistance, mosquito life cycles, and human behaviour to optimize control strategies. The results demonstrate that a combination of targeted insecticide application and community education significantly decreases malaria transmission rates, providing a comprehensive approach to managing this public health challenge. The study revealed that mathematical modelling can effectively predict changes in insecticide susceptibility among mosquito populations. Optimal control strategies were identified, which included targeted insecticide application and community education programs. These strategies significantly reduced the transmission rates of malaria, highlighting the importance of integrating scientific models with public health initiatives.

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    Applications of fixed point theorems in extended cone $ b $-metric spaces over Banach algebras to integral equations arising in signal processing

    by Nura Alotaibi, Jamshaid Ahmad

    The aim of this research article is to explore the notion of extended cone $ b $-metric spaces over Banach algebras and to establish new fixed point theorems for both single-valued mappings and multi-valued mappings. These results extend and generalize several well-known findings in metric fixed point theory. To demonstrate the applicability of our theoretical results, we provide illustrative examples that highlight the distinct features of our approach. Additionally, we showcase the practical relevance of our primary theorem by solving a Fredholm integral equation of the second kind, which arises in the context of radar and sonar signal processing.

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    Investigations into $ (n, q) $-symmetry in nonlinear multimappings acting on a metric space

    by Sid Ahmed Ould Ahmed Mahmoud, Nura Alotaibi, Sid Ahmed Ould Beinane

    In light of recent advances, this paper introduces a novel class of multimappings within the framework of metric spaces that aims to deepen the understanding of the structure and interplay of symmetric commuting tuples of mappings. A central focus of our study is the analysis of the product of two symmetric commuting tuples of mappings (c.t.m): Specifically, we consider an $(m, q)$-symmetric c.t.m ${{\bf N}} = (\mathcal{N}_1, \dots, \mathcal{N}_p)$ and an $(n, q)$-symmetric c.t.m ${\bf W} = (\mathcal{W}_1, \dots, \mathcal{W}_r)$, and establish the precise conditions under which their product ${\bf N} \odot {\bf W}$ yields an $(m+n-1, q)$-symmetric c.t.m. In addition, we investigate the behavior of $(m, q)$-isometric commuting tuples under composition ${\bf N} \cdot {\bf W}$, deriving new results that generalize existing theorems in the literature, most notably extending of Theorem 2.14 in Bermúdez et al., J. Operat. Theor., 72(2) (2014), 313–329 to a broader setting. The analysis of mappings in metric spaces is inherently complex, as these spaces often lack algebraic structures such as vector addition or scalar multiplication, making the study of nonlinear and multimappings particularly challenging. Our findings contribute to this area by elucidating the subtle relationships among symmetry, isometry, and commutativity in mapping tuples, thereby enabling more structured approaches to higher-dimensional problems within this framework.