Browsing by Author "Almalahi, Mohammed A."

Now showing 1 - 7 of 7

Citation - WoS: 6
Citation - Scopus: 6
Multipoint BVP for the Langevin Equation under ϕ -Hilfer Fractional Operator
(Wiley, 2022) Almalahi, Mohammed A.; Jarad, Fahd; Panchal, Satish K.; Jarad, Fahd; 234808; Matematik
In this research paper, we consider a class of boundary value problems for a nonlinear Langevin equation involving two generalized Hilfer fractional derivatives supplemented with nonlocal integral and infinite-point boundary conditions. At first, we derive the equivalent solution to the proposed problem at hand by relying on the results and properties of the generalized fractional calculus. Next, we investigate and develop sufficient conditions for the existence and uniqueness of solutions by means of semigroups of operator approach and the Krasnoselskii fixed point theorems as well as Banach contraction principle. Moreover, by means of Gronwall's inequality lemma and mathematical techniques, we analyze Ulam-Hyers and Ulam-Hyers-Rassias stability results. Eventually, we construct an illustrative example in order to show the applicability of key results.
Citation - WoS: 2
Citation - Scopus: 2
New results for a coupled system of abr fractional differential equations with sub-strip boundary conditions
(Amer inst Mathematical Sciences-aims, 2022) Almalahi, Mohammed A.; Jarad, Fahd; Panchal, Satish K.; Aljaaidi, Tariq A.; Jarad, Fahd; 234808; Matematik
In this article, we investigate sufficient conditions for the existence, uniqueness and UlamHyers (UH) stability of solutions to a new system of nonlinear ABR fractional derivative of order 1 < e <= 2 subjected to multi-point sub-strip boundary conditions. We discuss the existence and uniqueness of solutions with the assistance of Leray-Schauder alternative theorem and Banach's contraction principle. In addition, by using some mathematical techniques, we examine the stability results of Ulam-Hyers (UH). Finally, we provide one example in order to show the validity of our results.
Citation - WoS: 3
Citation - Scopus: 4
On Atangana-Baleanu-Type Nonlocal Boundary Fractional Differential Equations
(Wiley, 2022) Jarad, Fahd; Panchal, Satish K.; Abdo, Mohammed S.; Jarad, Fahd; 234808; Matematik
This research paper is devoted to investigating two classes of boundary value problems for nonlinear Atangana-Baleanu-type fractional differential equations with Atangana-Baleanu fractional integral conditions. The applied fractional derivatives work as the nonlocal and nonsingular kernel. Upon using Krasnoselskii's and Banach's fixed point techniques, we establish the existence and uniqueness of solutions for proposed problems. Moreover, the Ulam-Hyers stability theory is constructed by using nonlinear analysis. Eventually, we provide two interesting examples to illustrate the effectiveness of our acquired results.
Citation - WoS: 7
Citation - Scopus: 7
Qualitative analysis of a fuzzy Volterra-Fredholm integrodifferential equation with an Atangana-Baleanu fractional derivative
(Amer inst Mathematical Sciences-aims, 2022) Jarad, Fahd; Almalahi, Mohammed A.; Panchal, Satish K.; Abdeljawad, Thabet; Jarad, Fahd; Abdo, Mohammed S.; Shah, Kamal; Abdeljawad, Thabet; 234808; Matematik
The point of this work was to analyze and investigate the sufficient conditions of the existence and uniqueness of solutions for the nonlinear fuzzy fractional Volterra Fredholm integrodifferential equation in the frame of the Atangana-Baleanu-Caputo fractional derivative methodology. To begin with, we give the parametric interval form of the Atangana-Baleanu-Caputo fractional derivative on fuzzy set-valued functions. Then, by employing Schauder???s and Banach???s fixed point procedures, we examine the existence and uniqueness of solutions for fuzzy fractional Volterra Fredholm integro-differential equation with the Atangana-Baleanu-Caputo fractional operator. It turns out that the last interval model is a combined arrangement of nonlinear equations. In addition, we consider results by applying the Adams Bashforth fractional technique and present two examples that have been numerically solved using graphs.
Citation - WoS: 8
Citation - Scopus: 9
Results on Implicit Fractional Pantograph Equations with Mittag-Leffler Kernel and Nonlocal Condition
(Wiley, 2022) Almalahi, Mohammed A.; Jarad, Fahd; Panchal, Satish K.; Jarad, Fahd; 234808; Matematik
In this study, the main focus is on an investigation of the sufficient conditions of existence and uniqueness of solution for two-classess of nonlinear implicit fractional pantograph equations with nonlocal conditions via Atangana-Baleanu-Riemann-Liouville (ABR) and Atangana-Baleanu-Caputo (ABC) fractional derivative with order sigma is an element of 1,2. We introduce the properties of solutions as well as stability results for the proposed problem without using the semigroup property. In the beginning, we convert the given problems into equivalent fractional integral equations. Then, by employing some fixed-point theorems such as Krasnoselskii and Banach's techniques, we examine the existence and uniqueness of solutions to proposed problems. Moreover, by using techniques of nonlinear functional analysis, we analyze Ulam-Hyers (UH) and generalized Ulam-Hyers (GUH) stability results. As an application, we provide some examples to illustrate the validity of our results.
Citation - WoS: 19
Citation - Scopus: 20
Stability results of positive solutions for a system of ψ -Hilfer fractional differential equations
(Pergamon-elsevier Science Ltd, 2021) Almalahi, Mohammed A.; Jarad, Fahd; Panchal, Satish K.; Jarad, Fahd; 234808; Matematik
The major objective of this work is to investigate sufficient conditions of existence and uniqueness of positive solutions for a finite system of psi-Hilfer fractional differential equations. The gained results are obtained by building the upper and lower control functions of the nonlinear expression with the help of fixed point theorems such as Banach and Schauder. Furthermore, we establish various kinds of Ulam stability results by applying the techniques of nonlinear functional analysis. A pertinent example is provided to corroboration of the results obtained. (C) 2021 Elsevier Ltd. All rights reserved.
Citation - WoS: 10
Citation - Scopus: 10
Ulam–Hyers–Mittag-Leffler stability for tripled system of weighted fractional operator with TIME delay
(Springer, 2021) Jarad, Fahd; Almalahi, Mohammed A.; Panchal, Satish K.; Abdeljawad, Thabet; Jarad, Fahd; Abdeljawad, Thabet; 234808; Matematik
This study is aimed to investigate the sufficient conditions of the existence of unique solutions and the Ulam-Hyers-Mittag-Leffler (UHML) stability for a tripled system of weighted generalized Caputo fractional derivatives investigated by Jarad et al. (Fractals 28:2040011 2020) in the frame of Chebyshev and Bielecki norms with time delay. The acquired results are obtained by using Banach fixed point theorems and the Picard operator (PO) method. Finally, a pertinent example of the results obtained is demonstrated.