Browsing by Author "Abdo, Mohammed S."

Now showing 1 - 7 of 7

Citation - WoS: 8
Citation - Scopus: 2
An Analytical Study Of Fractional Delay Impulsive Implicit Systems With Mittag-Leffler Law
(Ministry Communications & High Technologies Republic Azerbaijan, 2023) Abdeljawad, Thabet; Abdeljawad, Thabet; Shah, Kamal; Jarad, Fahd; Abdo, Mohammed S.; Jarad, Fahd; 234808; Matematik
The Atangana-Baleanu-Caputo fractional derivative is a novel operator with a non-singular Mittag-Leffler kernel that we use to solve a class of Cauchy problems for delay impulsive implicit fractional differential equations. We also show the existence and uniqueness of the solution to the proposed problem. Our study makes use of the Gro center dot nwall inequality in the context of the Atangana-Baleanu fractional integral. Additionally, by the use of fixed point theorems due to Banach, Schaefer, and nonlinear functional analysis, necessary and sufficient conditions are developed under which the considered problem has at least one solution. By providing a relevant example, the results are demonstrated.
Citation - WoS: 37
Citation - Scopus: 42
Existence of positive solutions for weighted fractional order differential equations
(Pergamon-elsevier Science Ltd, 2020) Abdeljawad, Thabet; Abdo, Mohammed S.; Abdeljawad, Thabet; Jarad, Fahd; Ali, Saeed M.; Shah, Kamal; Jarad, Fahd; 234808; Matematik
In this paper, we deliberate two classes of initial value problems for nonlinear fractional differential equations under a version weighted generalized of Caputo fractional derivative given by Jarad et al. (2020a) [25]. We get a formula for the solution through the equivalent fractional integral equations to the proposed problems. The existence and uniqueness of positive solutions have been obtained by using lower and upper solutions. The acquired results are demonstrated by building the upper and lower control functions of the nonlinear term with the aid of Banach and Schauder fixed point theorems. The acquired results are demonstrated by pertinent numerical examples along with the Bashforth Moulton prediction correction scheme and Matlab. (C) 2020 Elsevier Ltd. All rights reserved.
Citation - WoS: 4
Citation - Scopus: 4
Nonexistence results of Caputo-type fractional problem
(Springer, 2021) Kassim, Mohammed D.; Jarad, Fahd; Ali, Saeed M.; Abdo, Mohammed S.; Jarad, Fahd; 234808; Matematik
In this paper, we deal with Caputo-type fractional differential inequality where there is a low-order fractional derivative with the term polynomial source. We investigate the nonexistence of nontrivial global solutions in a suitable space via the test function technique and some properties of fractional integrals. Finally, we demonstrate three examples to illustrate our results. The presented results are more general than those in the literature, which can be obtained as particular cases.
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: 1
Citation - Scopus: 2
Semilinear fractional evolution inclusion problem in the frame of a generalized Caputo operator
(Hindawi Ltd, 2021) Lachouri, Adel; Jarad, Fahd; Ardjouni, Abdelouaheb; Jarad, Fahd; Abdo, Mohammed S.; 234808; Matematik
In this paper, we study the existence of solutions to initial value problems for a nonlinear generalized Caputo fractional differential inclusion with Lipschitz set-valued functions. The applied fractional operator is given by the kernel kd/d rho. The existence result is obtained via fixed point theorems due to Covitz and Nadler. Moreover, we also characterize the topological properties of the set of solutions for such inclusions. The obtained results generalize previous works in the literature, where the classical Caputo fractional derivative is considered. In the end, an example demonstrating the effectiveness of the theoretical results is presented.
Citation - WoS: 35
Citation - Scopus: 38
Study of impulsive problems under Mittag-Leffler power law
(Elsevier Sci Ltd, 2020) Abdeljawad, Thabet; Abdo, Mohammed S.; Abdeljawad, Thabet; Jarad, Fahd; Shah, Kamal; Jarad, Fahd; 234808; Matematik
This article is fundamentally concerned with deriving the solution formula, existence, and uniqueness of solutions of two types of Cauchy problems for impulsive fractional differential equations involving Atangana-Baleanu-Caputo (ABC) fractional derivative which possesses nonsingular Mittag-Leffler kernel. Our investigation is based on nonlinear functional analysis and some fixed point techniques. Besides, some examples are given delineated to illustrate the effectiveness of our outcome.