Browsing by Author "Abdeljawad, Thabet"

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A common fixed point theorem of a Greguš type on convex cone metric spaces
(2011) Abdeljawad, Thabet; Karapinar, Erdal
The result of Ćirić [1] on a common fixed point theorem of Greguš type on metric spaces is extended to the class of cone metric spaces. Namely, a common fixed point theorem is proved in s-convex cone metric spaces under the normality of the cone and another common fixed point theorem is proved in convex cone metric spaces under the assumption that the cone is strongly minihedral.
A common fixed point theorem of a Gregus type on convex cone metric spaces
(Eudoxus Press, 2011) Abdeljawad, Thabet; Karapınar, Erdal
The result of Ciric [1] on a common fixed point theorem of Gregus-type on metric spaces is extended to the class of cone metric spaces. Namely, a common fixed point theorem is proved in s-convex cone metric spaces under the normality of the cone and another common fixed point theorem is proved in convex cone metric spaces under the assumption that the cone is strongly minihedral
A Gap in the Paper A Note On Cone Metric Fixed Point Theory and Its Equivalence [Nonlinear Anal. 72(5), (2010), 2259-2261]
(Gazi Univ, 2011) Abdeljawad, Thabet; Karapınar, Erdal
There is a gap in Theorem 2.2 of the paper of Du [1]. In this paper, we shall state the gap and repair it.
A note on the chain rule on time scales
(Çankaya Üniversitesi, 2008) Abdeljawad, Thabet
It is known, in general, that the chain rule on general time scale derivatives does not behave well as in the case of usual derivative. However, we discuss some special cases where the time scale derivative has the usual chain rule. The results are analyzed for both the delta and nabla time scales derivatives.
A pair of Köthe spaces between which all continuous linear operators are bounded
(2004) Abdeljawad, Thabet
Citation - WoS: 27
Citation - Scopus: 27
Almost Periodic Dynamics of a Discrete Nicholson's Blowflies Model Involving a Linear Harvesting Term
(Springer, 2012) Abdeljawad, Thabet; Alzabut, Jehad; Bolat, Yasar
We consider a discrete Nicholson's blowflies model involving a linear harvesting term. Under appropriate assumptions, sufficient conditions are established for the existence and exponential convergence of positive almost periodic solutions of this model. To expose the effectiveness of the main theorems, we support our result by a numerical example.
Citation - Scopus: 1
Alpha Fractional Frequency Laplace Transform Through Multiseries
(Springer, 2020) Gnanaprakasam, Britto Antony Xavier; Jarad, Fahd; Murugesan, Meganathan; Abdeljawad, Thabet
Our main goal in this work is to derive the frequency Laplace transforms of the products of two and three functions with tuning factors. We propose the Laplace transform for certain types of multiseries of circular functions as well. For use in numerical results, we derive a finite summation formula and m-series formulas. Moreover, we discuss various explanatory examples.
Citation - WoS: 47
Citation - Scopus: 53
Analysis of Some Generalized Abc - Fractional Logistic Models
(Elsevier, 2020) Al-Mdallal, Qasem M.; Jarad, Fahd; Abdeljawad, Thabet; Hajji, Mohamed A.
In this article, some logistic models in the settings of Caputo fractional operators with multi-parametered Mittag-Leffler kernels (ABC) are studied. This study mainly focuses on modified quadratic and cubic logistic models in the presence of a Caputo type fractional derivative. Existence and uniqueness theorems are proved and stability analysis is discussed by perturbing the equilib-rium points. Numerical illustrative examples are discussed for the studied models. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
Citation - WoS: 6
Citation - Scopus: 8
Analytic and Numerical Solutions of Discrete Bagley-Torvik Equation
(Springer, 2021) Khashan, M. Motawi; Xavier, Gnanaprakasam Britto Antony; Jarad, Fahd; Meganathan, Murugesan; Abdeljawad, Thabet; Britto Antony Xavier, Gnanaprakasam; Motawi Khashan, M.
In this research article, a discrete version of the fractional Bagley-Torvik equation is proposed: del(2)(h)u(t) + A(C)del(nu)(h) u(t) + Bu(t) = f (t), t > 0, (1) where 0 < nu < 1 or 1 < nu < 2, subject to u(0) = a and del(h)u(0) = b, with a and b being real numbers. The solutions are obtained by employing the nabla discrete Laplace transform. These solutions are expressed in terms of Mittag-Leffler functions with three parameters. These solutions are handled numerically for some examples with specific values of some parameters.
Citation - WoS: 23
Citation - Scopus: 17
An Analytical Study of Fractional Delay Impulsive Implicit Systems With Mittag-Leffler Law
(Ministry Communications & High Technologies Republic Azerbaijan, 2023) Abdo, Mohammed S.; Jarad, Fahd; Abdeljawad, Thabet; Shah, Kamal
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: 109
Citation - Scopus: 113
Applying New Fixed Point Theorems on Fractional and Ordinary Differential Equations
(Springer, 2019) Karapinar, Erdal; Abdeljawad, Thabet; Jarad, Fahd
In this paper, we consider a fixed point theorem that extends and unifies several existing results in the literature. We apply the proven fixed point results on the existence of solution of ordinary boundary value problems and fractional boundary value problems with integral type boundary conditions in the frame of some Caputo type fractional operators.
Citation - WoS: 17
Citation - Scopus: 13
Best Proximity Points for Cyclical Contraction Mappings With 0-Boundedly Compact Decompositions
(Eudoxus Press, Llc, 2013) Abdeljawad, Thabet; Abdeljawad, T.; Alzabut, J. O.; Alzabut, Jehad; Mukheimer, A.; Zaidan, Y.; Matematik
The existence of best proximity points for cyclical type contraction mappings is proved in the category of partial metric spaces. The concept of 0-boundedly compact is introduced and used in the cyclical decomposition. Some possible generalizations to the main results are discussed. Further, illustrative examples are given to demonstrate the effectiveness of our results.
Citation - WoS: 14
Citation - Scopus: 14
Boundary Value Problem of Weighted Fractional Derivative of a Function With a Respect To Another Function of Variable Order
(Springer, 2023) Jarad, Fahd; Alqudah, Manar A.; Abdeljawad, Thabet; Benia, Kheireddine; Souid, Mohammed Said
This study aims to resolve weighted fractional operators of variable order in specific spaces. We establish an investigation on a boundary value problem of weighted fractional derivative of one function with respect to another variable order function. It is essential to keep in mind that the symmetry of a transformation for differential equations is connected to local solvability, which is synonymous with the existence of solutions. As a consequence, existence requirements for weighted fractional derivative of a function with respect to another function of constant order are necessary. Moreover, the stability with in Ulam-Hyers-Rassias sense is reviewed. The outcomes are derived using the Kuratowski measure of non-compactness. A model illustrates the trustworthiness of the observed results.
Citation - WoS: 31
Citation - Scopus: 32
Bounds of Generalized Proportional Fractional Integrals in General Form Via Convex Functions and Their Applications
(Mdpi, 2020) Jarad, Fahd; Nisar, Kottakkaran Sooppy; Rahman, Gauhar; Abdeljawad, Thabet
In this paper, our objective is to apply a new approach to establish bounds of sums of left and right proportional fractional integrals of a general type and obtain some related inequalities. From the obtained results, we deduce some new inequalities for classical generalized proportional fractional integrals as corollaries. These inequalities have a connection with some known and existing inequalities which are mentioned in the literature. In addition, some applications of the main results are presented.
Citation - WoS: 6
Citation - Scopus: 6
A Caputo Fractional Order Boundary Value Problem With Integral Boundary Conditions
(Eudoxus Press, Llc, 2013) Babakhani, Azizollah; Abdeljawad, Thabet; Abdeljawad, Thabet; Matematik
In this paper, we discuss existence and uniqueness of solutions to nonlinear fractional order ordinary differential equations with integral boundary conditions in an ordered Banach space. We use the Caputo fractional differential operator and the nonlinearity depends on the fractional derivative of an unknown function. The nonlinear alternative of the Leray- Schauder type Theorem is the main tool used here to establish the existence and the Banach contraction principle to show the uniqueness of the solution under certain conditions. The compactness of solutions set is also investigated and an example is included to show the applicability of our results.
Citation - WoS: 120
Citation - Scopus: 127
Caputo Q-Fractional Initial Value Problems and a Q-Analogue Mittag-Leffler Function
(Elsevier, 2011) Abdeljawad, Thabet; Baleanu, Dumitru
Caputo q-fractional derivatives are introduced and studied. A Caputo -type q-fractional initial value problem is solved and its solution is expressed by means of a new introduced q-Mittag-Leffler function. Some open problems about q-fractional integrals are proposed as well. (C) 2011 Elsevier B.V. All rights reserved.
Citation - WoS: 335
Citation - Scopus: 439
Caputo-Type Modification of the Hadamard Fractional Derivatives
(Springer international Publishing Ag, 2012) Jarad, Fahd; Abdeljawad, Thabet; Baleanu, Dumitru
Generalization of fractional differential operators was subjected to an intense debate in the last few years in order to contribute to a deep understanding of the behavior of complex systems with memory effect. In this article, a Caputo-type modification of Hadamard fractional derivatives is introduced. The properties of the modified derivatives are studied.
Citation - WoS: 68
Citation - Scopus: 67
Certain Inequalities Via Generalized Proportional Hadamard Fractional Integral Operators
(Springer, 2019) Jarad, Fahd; Khan, Aftab; Nisar, Kottakkaran Sooppy; Rahman, Gauhar; Abdeljawad, Thabet
In the article, we introduce the generalized proportional Hadamard fractional integrals and establish several inequalities for convex functions in the framework of the defined class of fractional integrals. The given results are generalizations of some known results.
Citation - WoS: 3
Certain Subclasses of Β-Uniformly Q-Starlike and Β-Uniformly Q-Convex Functions
(Hindawi Ltd, 2020) Abdeljawad, Thabet; Jarad, Fahd; AbuJarad, Eman S. A.; AbuJarad, Mohammed H. A.
In this paper, the authors introduced certain subclasses beta-uniformly q-starlike and beta-uniformly q-convex functions of order a involving the q-derivative operator defined in the open unit disc. Coefficient bounds were also investigated.
Citation - WoS: 10
Citation - Scopus: 11
Chaotic Attractors and Fixed Point Methods in Piecewise Fractional Derivatives and Multi-Term Fractional Delay Differential Equations
(Elsevier, 2023) Jarad, Fahd; Panda, Sumati Kumari; Abdeljawad, Thabet
Using generalized cyclic contractions, we establish some fixed point results in controlled rectangular metric spaces. Some subsequent outcomes are obtained. Moreover, some necessary conditions to demonstrate the existence of solutions for the multi-term fractional delay differential equations with wth order and the piecewise equations under the setting of non-singular type derivative are established in this paper. In order to demonstrate the effectiveness of our results, we provided some numerical examples.