Roshdi Khalil
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Roshdi Khalil has a total of 24 co-authors. Here are the top co-authors by number of shared publications:
- Ma’mon Abu Hammad
Department of Mathematics, Al-Zaytoonah University of Jordan, Amman 11733, Jordan
10 shared publications - Waseem Ghazi Alshanti
Department of Mathematics, Al Zaytoonah University of Jordan, Amman, Jordan
9 shared publications - Mohammed Al Horani
The University of Jordan
5 shared publications - Abdel Yousef
The University of Jordan
4 shared publications - Abdelrahman Yousef
Department of Mathematics and Statistics, College of Arts and Sciences, American University of Sharjah, Sharjah, UAE
2 shared publications - Ahmad Alshanty
Cyber security Department, Al Zaytoonah University of Jordan, Jordan
2 shared publications
Latest Publications
- Open Access
- 1 January 2026
- Published by Wiley in Journal of Function Spaces
- Vol. 2026 (1) , 6105189
Fractional Abstract Cauchy Problems of Second Order With Operator‐Valued Solutions
This paper examines a second‐order abstract Cauchy problem involving a conformable fractional derivative and a bounded linear operator that admits fractional powers. Under a simple norm condition on the operator, explicit formulas for homogeneous and inhomogeneous solutions are obtained by combining the operational calculus for A α with a variation of parameters argument adapted to the conformable setting. The resulting expressions give a direct representation of the solution in terms of operator exponentials and conformable integrals. An illustrative example is included to demonstrate the method in a concrete operator framework.
- 1 January 2026
- Published by Wiley in Journal of Function Spaces
- Vol. 2026 (1) , 6105189
Open AccessFractional Abstract Cauchy Problems of Second Order With Operator‐Valued Solutions
This paper examines a second‐order abstract Cauchy problem involving a conformable fractional derivative and a bounded linear operator that admits fractional powers. Under a simple norm condition on the operator, explicit formulas for homogeneous and inhomogeneous solutions are obtained by combining the operational calculus for A α with a variation of parameters argument adapted to the conformable setting. The resulting expressions give a direct representation of the solution in terms of operator exponentials and conformable integrals. An illustrative example is included to demonstrate the method in a concrete operator framework.
- Open Access
- 5 November 2025
- Published by New York Business Global LLC in European Journal of Pure and Applied Mathematics
- Vol. 18 (4) , 6557
A New Definition of (α, β)-Fractional Derivatives for Complex-Valued Functions and Their Analytic Properties
In this paper, we present a new definition for derivatives of complex fractional orders of complex valued functions. We introduce the concepts of both (a,B)-Cauchy-Riemann equtions and (a,B)-fractional analytic complex valued function.
- 5 November 2025
- Published by New York Business Global LLC in European Journal of Pure and Applied Mathematics
- Vol. 18 (4) , 6557
Open AccessA New Definition of (α, β)-Fractional Derivatives for Complex-Valued Functions and Their Analytic Properties
In this paper, we present a new definition for derivatives of complex fractional orders of complex valued functions. We introduce the concepts of both (a,B)-Cauchy-Riemann equtions and (a,B)-fractional analytic complex valued function.
- Open Access
- 5 November 2025
- Published by New York Business Global LLC in European Journal of Pure and Applied Mathematics
- Vol. 18 (4) , 6559
Second-Order Abstract Cauchy Problem in Two Variables
In this paper, we consider the following second-order abstract Cauchyproblem in two variables\begin{equation*}D_{ss}^{2}u(s,t)+D_{tt}^{2}u(s,t)+2D_{st}^{2}u(s,t)+A\left[D_{s}u(s,t)+D_{t}u(s,t)\right] =Bu(s,t),\end{equation*}where $A,B$ are closed linear operators on a Banach space $X$ such that\begin{eqnarray*}A &:&Dom(A)\subseteq X\rightarrow X, \\B &:&Dom(B)\subseteq X\rightarrow X,\end{eqnarray*}$u(s,t):\left[ 0,1\right] \times \left[ 0,1\right] \rightarrow X$ is anunknown twice-continuously partially differentiable function on $\left[ 0,1%\right] \times \left[ 0,1\right] \subseteq \mathbb{R}^{2}$ where $Rang(u)\subseteq Dom(A)\cap Dom(B)$. Utilizing properties of atomic operators, an atomic solution is obtained.- 5 November 2025
- Published by New York Business Global LLC in European Journal of Pure and Applied Mathematics
- Vol. 18 (4) , 6559
Open AccessSecond-Order Abstract Cauchy Problem in Two Variables
In this paper, we consider the following second-order abstract Cauchyproblem in two variables\begin{equation*}D_{ss}^{2}u(s,t)+D_{tt}^{2}u(s,t)+2D_{st}^{2}u(s,t)+A\left[D_{s}u(s,t)+D_{t}u(s,t)\right] =Bu(s,t),\end{equation*}where $A,B$ are closed linear operators on a Banach space $X$ such that\begin{eqnarray*}A &:&Dom(A)\subseteq X\rightarrow X, \\B &:&Dom(B)\subseteq X\rightarrow X,\end{eqnarray*}$u(s,t):\left[ 0,1\right] \times \left[ 0,1\right] \rightarrow X$ is anunknown twice-continuously partially differentiable function on $\left[ 0,1%\right] \times \left[ 0,1\right] \subseteq \mathbb{R}^{2}$ where $Rang(u)\subseteq Dom(A)\cap Dom(B)$. Utilizing properties of atomic operators, an atomic solution is obtained. - Open Access
- 1 January 2025
- Published by Wiley in Journal of Applied Mathematics
- Vol. 2025 (1)
Two‐Rank and Atomic Solutions of a Bateman–Burgers Type Equation via Functional Analytic Methods
In this paper, we derive both a two‐rank solution and an atomic solution for a Bateman–Burgers type partial differential equation. Specifically, we study an equation in which the second mixed derivative of the unknown function with respect to space and time, together with the second derivative in space, equals the second derivative in time. Using functional analysis techniques, particularly the Hahn–Banach theorem and tensor product theory, we construct explicit two‐rank and atomic solutions. These results illustrate how functional analytic tools provide alternative strategies for analyzing nonlinear equations where traditional separation of variables does not apply.
- 1 January 2025
- Published by Wiley in Journal of Applied Mathematics
- Vol. 2025 (1)
Open AccessTwo‐Rank and Atomic Solutions of a Bateman–Burgers Type Equation via Functional Analytic Methods
In this paper, we derive both a two‐rank solution and an atomic solution for a Bateman–Burgers type partial differential equation. Specifically, we study an equation in which the second mixed derivative of the unknown function with respect to space and time, together with the second derivative in space, equals the second derivative in time. Using functional analysis techniques, particularly the Hahn–Banach theorem and tensor product theory, we construct explicit two‐rank and atomic solutions. These results illustrate how functional analytic tools provide alternative strategies for analyzing nonlinear equations where traditional separation of variables does not apply.
- Open Access
- 1 December 2024
- Published by Vertex Academic Press in Gulf Journal of Mathematics
- Vol. 18 (1) , 189-196
Atomic solution for both ordinary and fractional abstract Cauchy problem in tensor product form
In this paper, we discuss the atomic solutions of the abstract Cauchy problem in two variables. The proposed abstract Cauchy problem is assumed to be non-homogeneous and in tensor product form. We utilize some results from the theory of tensor product of Banach spaces to obtain solutions in the atom operator form. The approach is applied for both ordinary and α-conformable fractional derivatives.
- 1 December 2024
- Published by Vertex Academic Press in Gulf Journal of Mathematics
- Vol. 18 (1) , 189-196
Open AccessAtomic solution for both ordinary and fractional abstract Cauchy problem in tensor product form
In this paper, we discuss the atomic solutions of the abstract Cauchy problem in two variables. The proposed abstract Cauchy problem is assumed to be non-homogeneous and in tensor product form. We utilize some results from the theory of tensor product of Banach spaces to obtain solutions in the atom operator form. The approach is applied for both ordinary and α-conformable fractional derivatives.
- Open Access
- 1 December 2024
- Published by Vertex Academic Press in Gulf Journal of Mathematics
- Vol. 18 (1) , 118-123
Hahn-Banach theorem-based analytic approaches for the abstract Cauchy-Euler differential equation
In this paper, we consider the following abstract Cauchy-Euler differential equation t2u''(t) + tu't) + u(t) = 0; where u: [0; t] -> X is an unknown function such that X is a Banach space. Utilizing the Hahn-Banach Theorem, two analytic approaches are presented.
- 1 December 2024
- Published by Vertex Academic Press in Gulf Journal of Mathematics
- Vol. 18 (1) , 118-123
Open AccessHahn-Banach theorem-based analytic approaches for the abstract Cauchy-Euler differential equation
In this paper, we consider the following abstract Cauchy-Euler differential equation t2u''(t) + tu't) + u(t) = 0; where u: [0; t] -> X is an unknown function such that X is a Banach space. Utilizing the Hahn-Banach Theorem, two analytic approaches are presented.
- Open Access
- 31 October 2024
- Published by New York Business Global LLC in European Journal of Pure and Applied Mathematics
- Vol. 17 (4) , 2492-2504
Common Fixed Point of Generalized Berinde Type Contraction and an Application
In this paper, we introduce $\lambda_{(s,\varphi,\psi,L)}$-generalized Berinde type contraction and obtain some common fixed point results for such class of contractions the setting of triangular $\alpha$-admissible mappings with respect to $\eta$ in the framework of $b$-metric spaces. Our results generalize and extend some theorems in the literature. An example is given to support our result.- 31 October 2024
- Published by New York Business Global LLC in European Journal of Pure and Applied Mathematics
- Vol. 17 (4) , 2492-2504
Open AccessCommon Fixed Point of Generalized Berinde Type Contraction and an Application
In this paper, we introduce $\lambda_{(s,\varphi,\psi,L)}$-generalized Berinde type contraction and obtain some common fixed point results for such class of contractions the setting of triangular $\alpha$-admissible mappings with respect to $\eta$ in the framework of $b$-metric spaces. Our results generalize and extend some theorems in the literature. An example is given to support our result. - Open Access
- 31 October 2024
- Published by New York Business Global LLC in European Journal of Pure and Applied Mathematics
- Vol. 17 (4) , 2985-2989
Every Uniquely Remotal Set in a Hilbert Space is aSingleton
In this paper we prove that every uniquely remotal set in a Hilbert space is a singleton.
- 31 October 2024
- Published by New York Business Global LLC in European Journal of Pure and Applied Mathematics
- Vol. 17 (4) , 2985-2989
Open AccessEvery Uniquely Remotal Set in a Hilbert Space is aSingleton
In this paper we prove that every uniquely remotal set in a Hilbert space is a singleton.
- Open Access
The Invariant Subspace Problem for Separable Hilbert Spaces
In this paper, we prove that every bounded linear operator on a separable Hilbert space has a non-trivial invariant subspace. This answers the well-known invariant subspace problem.
Open AccessThe Invariant Subspace Problem for Separable Hilbert Spaces
In this paper, we prove that every bounded linear operator on a separable Hilbert space has a non-trivial invariant subspace. This answers the well-known invariant subspace problem.
- Open Access
- 1 January 2024
- Published by Wiley in Journal of Applied Mathematics
- Vol. 2024 (1)
Tensor Product Technique and Atomic Solution of Fractional Partial Differential Equations
In this paper, we investigate the atomic solution of a special type of fractional partial differential equations. Tensor product in Banach spaces, some properties of atom operators, and some properties of conformable fractional derivatives are utilized in such process.JEL Classification: 34G10, 34A55
- 1 January 2024
- Published by Wiley in Journal of Applied Mathematics
- Vol. 2024 (1)
Open AccessTensor Product Technique and Atomic Solution of Fractional Partial Differential Equations
In this paper, we investigate the atomic solution of a special type of fractional partial differential equations. Tensor product in Banach spaces, some properties of atom operators, and some properties of conformable fractional derivatives are utilized in such process.JEL Classification: 34G10, 34A55