Abdeljawad, Thabet

Abdeljawad, Thabet

Job Title

Doç. Dr.

Email Address

thabet@cankaya.edu.tr

Main Affiliation

Matematik

Status

Former Staff

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Scholarly Output

171

Articles

331

Citation Count

10012

Supervised Theses

0 Scholarly Output Search Results

Now showing 1 - 10 of 170

Citation - WoS: 45
Citation - Scopus: 47
Fractional Proportional Differences With Memory
(Springer Heidelberg, 2017) Abdeljawad, Thabet; Abdeljawad, Thabet; Jarad, Fahd; Jarad, Fahd; Alzabut, Jehad; Alzabut, Jehad; 234808; Matematik
In this paper, we formulate nabla fractional sums and differences and the discrete Laplace transform on the time scale hZ. Based on a local type h-proportional difference (without memory), we generate new types of fractional sums and differences with memory in two parameters which are generalizations to the formulated fractional sums and differences. The kernel of the newly defined generalized fractional sum and difference operators contain h-discrete exponential functions. The discrete h-Laplace transform and its convolution theorem are then used to study the newly introduced discrete fractional operators and also used to solve Cauchy linear fractional difference type problems with step 0 < h <= 1.
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.
Citation - WoS: 62
Citation - Scopus: 79
Meir-Keeler alpha-contractive fixed and common fixed point theorems
(Springer international Publishing Ag, 2013) Abdeljawad, Thabet; Abdeljawad, Thabet; Matematik
Generalized Meir-Keeler alpha-contractive functions and pairs are introduced and their fixed and common fixed point theorems are obtained. Also, the so-called generalized Meir-Keeler alpha-f-contractive maps commuting with f are introduced and their coincidence and common fixed point theorems are investigated. New sufficient conditions different from those in (Samet et al. in Nonlinear Anal. 75:2154-2165, 2012) are used. An application to the coupled fixed point is established as well. An example is given to show that the alpha-Meir-Keeler generalization is real. AMS Subject Classification: 47H10, 54H25.
Citation - WoS: 86
Citation - Scopus: 78
Monotonicity analysis of a nabla discrete fractional operator with discrete Mittag-Leffler kernel
(Pergamon-elsevier Science Ltd, 2017) Abdeljawad, Thabet; Abdeljawad, Thabet; Baleanu, Dumitru; Baleanu, Dumitru; 56389; Matematik
Discrete fractional calculus is one of the new trends in fractional calculus both from theoretical and applied viewpoints. In this article we prove that if the nabla fractional difference operator with discrete Mittag-Leffler kernel ((ABR)(a -1) del(alpha)y) (t) of order 0 < alpha < 1/2 and starting at a - 1 is positive, then y(t) is alpha(2)- increasing. That is y (t + 1) >= alpha(2)y(t) for all t is an element of N-a = {a, a + 1,...}. Conversely, if y(t) is increasing and y(a) >= 0, then ((ABR)(a-1)del(alpha)y)(t) >= 0. The monotonicity properties of the Caputo and right fractional differences are concluded as well. As an application, we prove a fractional difference version of mean-value theorem. Finally, some comparisons to the classical discrete fractional case and to fractional difference operators with discrete exponential kernel are made. (C) 2017 Elsevier Ltd. All rights reserved.
Citation - WoS: 94
Citation - Scopus: 101
Mittag-Leffler stability analysis of fractional discrete-time neural networks via fixed point technique
(inst Mathematics & informatics, 2019) Abdeljawad, Thabet; Wu, Guo-Cheng; Abdeljawad, Thabet; Baleanu, Dumitru; Liu, Jinliang; Baleanu, Dumitru; Wu, Kai-Teng; 56389; Matematik
A class of semilinear fractional difference equations is introduced in this paper. The fixed point theorem is adopted to find stability conditions for fractional difference equations. The complete solution space is constructed and the contraction mapping is established by use of new equivalent sum equations in form of a discrete Mittag-Leffler function of two parameters. As one of the application, finite-time stability is discussed and compared. Attractivity of fractional difference equations is proved, and Mittag-Leffler stability conditions are provided. Finally, the stability results are applied to fractional discrete-time neural networks with and without delay, which show the fixed point technique's efficiency and convenience.
On a new class of fractional operators
(2017) Jarad, Fahd; Uğurlu, Ekin; Abdeljawad, Thabet; Baleanu, Dumitru; 56389; Matematik
This manuscript is based on the standard fractional calculus iteration procedure on conformable derivatives. We introduce new fractional integration and differentiation operators. We define spaces and present some theorems related to these operators.
Citation - WoS: 84
Qualitative Analysis of a Mathematical Model in the Time of COVID-19
(Hindawi Ltd, 2020) Abdeljawad, Thabet; Shah, Kamal; Abdeljawad, Thabet; Jarad, Fahd; Mahariq, Ibrahim; Jarad, Fahd; 234808; Matematik
In this article, a qualitative analysis of the mathematical model of novel corona virus named COVID-19 under nonsingular derivative of fractional order is considered. The concerned model is composed of two compartments, namely, healthy and infected. Under the new nonsingular derivative, we, first of all, establish some sufficient conditions for existence and uniqueness of solution to the model under consideration. Because of the dynamics of the phenomenon when described by a mathematical model, its existence must be guaranteed. Therefore, via using the classical fixed point theory, we establish the required results. Also, we present the results of stability of Ulam's type by using the tools of nonlinear analysis. For the semianalytical results, we extend the usual Laplace transform coupled with Adomian decomposition method to obtain the approximate solutions for the corresponding compartments of the considered model. Finally, in order to support our study, graphical interpretations are provided to illustrate the results by using some numerical values for the corresponding parameters of the model.
Citation - WoS: 24
Citation - Scopus: 26
Existence and Uniqueness of Uncertain Fractional Backward Difference Equations of Riemann-Liouville Type
(Hindawi Ltd, 2020) Abdeljawad, Thabet; Mohammed, Pshtiwan Othman; Abdeljawad, Thabet; Jarad, Fahd; Jarad, Fahd; Chu, Yu-Ming; 234808; Matematik
In this article, we consider the analytic solutions of the uncertain fractional backward difference equations in the sense of Riemann-Liouville fractional operators which are solved by using the Picard successive iteration method. Also, we consider the existence and uniqueness theorem of the solution to an uncertain fractional backward difference equation via the Banach contraction fixed-point theorem under the conditions of Lipschitz constant and linear combination growth. Finally, we point out some examples to confirm the validity of the existence and uniqueness of the solution.
Citation - WoS: 6
Citation - Scopus: 7
Lyapunov type inequality in the frame of Generalized caputo derivatives
(Amer inst Mathematical Sciences-aims, 2021) Jarad, Fahd; Jarad, Fahd; Adjabi, Yassine; Abdeljawad, Thabet; Abdeljawad, Thabet; Mallak, Saed F.; Alrabaiah, Hussam; 234808; Matematik
In this paper, we establish the Lyapunov-type inequality for boundary value problems involving generalized Caputo fractional derivatives that unite the Caputo and Caputo-Hadamrad fractional derivatives. An application about the zeros of generalized types of Mittag-Leffler functions is given.
Citation - WoS: 6
Citation - Scopus: 6
Order norm completions of cone metric spaces
(Taylor & Francis inc, 2011) Abdeljawad, Thabet; Abdeljawad, Thabet; Matematik
In this article, a completion theorem for cone metric spaces and a completion theorem for cone normed spaces are proved. The completion spaces are constructed by means of an equivalence relation defined via an ordered cone norm on the Banach space E whose cone is strongly minihedral and ordered closed. This order norm has to satisfy the generalized absolute value property. In particular, if E is a Dedekind complete Banach lattice, then, together with its absolute value norm, satisfy the desired properties.