Browsing by Author "Abdeljawad, Thabet"

Now showing 1 - 20 of 161

Citation - WoS: 16
Citation - Scopus: 19
Lyapunov Type Inequalities Via Fractional Proportional Derivatives and Application on the Free Zero Disc of Kilbas-Saigo Generalized Mittag-Leffler Functions
(Springer Heidelberg, 2019) Alzabut, Jehad; Abdeljawad, Thabet; Jarad, Fahd; Mallak, Saed F.
.In this article, we prove Lyapunov type inequalities for a nonlocal fractional derivative, called fractional proportional derivative, generated by modified conformable or proportional derivatives in both Riemann-Liuoville and Caputo senses. Further, in the Riemann-Liuoville case we prove a Lyapunov inequality for a fractional proportional weighted boundary value problem and apply it on a weighted Sturm-Liouville problem to estimate an upper bound for the free zero disk of the Kilbas-Saigo Mittag-Leffler functions of three parameters. The proven results generalize and modify previously obtained results in the literature.
Citation - WoS: 10
Citation - Scopus: 13
On a New Fixed Point Theorem With an Application on a Coupled System of Fractional Differential Equations
(Springer, 2020) Abdeljawad, Thabet; Afshari, Hojjat; Jarad, Fahd
In this work, new theorems and results related to fixed point theory are presented. The results obtained are used for the sake of proving the existence and uniqueness of a positive solution of a coupled system of equations that involves fractional derivatives in the Riemann-Liouville settings and is subject to boundary conditions in the form of integrals.
Citation - WoS: 8
Citation - Scopus: 15
Computation of Iterative Solutions Along With Stability Analysis To a Coupled System of Fractional Order Differential Equations
(Springeropen, 2019) Abdeljawad, Thabet; Shah, Kamal; Jarad, Fahd; Arif, Muhammad; Ali, Sajjad
In this research article, we investigate sufficient results for the existence, uniqueness and stability analysis of iterative solutions to a coupled system of the nonlinear fractional differential equations (FDEs) with highier order boundary conditions. The foundation of these sufficient techniques is a combination of the scheme of lower and upper solutions together with the method of monotone iterative technique. With the help of the proposed procedure, the convergence criteria for extremal solutions are smoothly achieved. Furthermore, a major aspect is devoted to the investigation of Ulam-Hyers type stability analysis which is also established. For the verification of our work, we provide some suitable examples along with their graphical represntation and errors estimates.
Citation - WoS: 7
Citation - Scopus: 6
Perron's Theorem for Q-Delay Difference Equations
(Natural Sciences Publishing Corp-nsp, 2011) Alzabut, Jehad; Alzabut, J. O.; Abdeljawad, T.; Abdeljawad, Thabet; Matematik
In this paper, we prove that if a linear q-delay difference equation satisfies Perron's condition then its trivial solution is uniformly asymptotically stable.
Citation - WoS: 19
Citation - Scopus: 29
Common Fixed Points of Generalized Meir-Keeler Α-Contractions
(Springer int Publ Ag, 2013) Abdeljawad, Thabet; Gopal, Dhananjay; Patel, Deepesh Kumar
Motivated by Abdeljawad (Fixed Point Theory Appl. 2013:19, 2013), we establish some common fixed point theorems for three and four self-mappings satisfying generalized Meir-Keeler alpha-contraction in metric spaces. As a consequence, the results of Rao and Rao (Indian J. Pure Appl. Math. 16(1):1249-1262, 1985), Jungck (Int. J. Math. Math. Sci. 9(4):771-779, 1986), and Abdeljawad itself are generalized, extended and improved. Sufficient examples are given to support our main results.
Citation - WoS: 44
Citation - Scopus: 66
Fractional Variational Principles With Delay
(Iop Publishing Ltd, 2008) Jarad, Fahd; Baleanu, Dumitru; Abdeljawad, Thabet
The fractional variational principles within Riemann-Liouville fractional derivatives in the presence of delay are analyzed. The corresponding Euler Lagrange equations are obtained and one example is analyzed in detail.
Citation - WoS: 12
Citation - Scopus: 14
Variational Principles in the Frame of Certain Generalized Fractional Derivatives
(Amer inst Mathematical Sciences-aims, 2020) Jarad, Fahd; Abdeljawad, Thabet
In this article, we study generalized fractional derivatives that contain kernels depending on a function on the space of absolute continuous functions. We generalize the Laplace transform in order to be applicable for the generalized fractional integrals and derivatives and apply this transform to solve some ordinary differential equations in the frame of the fractional derivatives under discussion.
Citation - WoS: 42
Citation - Scopus: 41
The Q-Fractional Analogue for Gronwall-Type Inequality
(Hindawi Publishing Corporation, 2013) Abdeljawad, Thabet; Alzabut, Jehad O.
We utilize q-fractional Caputo initial value problems of order 0 < alpha <= 1 to derive a.. -analogue for Gronwall-type inequality. Some particular cases are derived where q-Mittag-Leffler functions and q-exponential type functions are used. An example is given to illustrate the validity of the derived inequality.
Citation - WoS: 25
Citation - Scopus: 26
On Dynamic Systems in the Frame of Singular Function Dependent Kernel Fractional Derivatives
(Mdpi, 2019) Jarad, Fahd; Sene, Ndolane; Abdeljawad, Thabet; Madjidi, Fadila
In this article, we discuss the existence and uniqueness theorem for differential equations in the frame of Caputo fractional derivatives with a singular function dependent kernel. We discuss the Mittag-Leffler bounds of these solutions. Using successive approximation, we find a formula for the solution of a special case. Then, using a modified Laplace transform and the Lyapunov direct method, we prove the Mittag-Leffler stability of the considered system.
Citation - Scopus: 5
A Frational Finite Differene Inclusion
(Eudoxus Press, LLC, 2016) Baleanu, D.; Abdeljawad, Thabet; Rezapour, S.; Baleanu, Dumitru; Salehi, S.; Matematik
In this manuscript, we investigated the fractional finite difference inclusion (formula presented) via the boundary conditions Δx(b+μ)=A and x(μ-2)=B, where 1 < μ ≤ 2, A, B ε ℝ. and (formula presented) is a compact valued multifunction. © 2016 by Eudoxus Press, LLC, All rights reserved.
On a new class of fractional operators
(2017) Jarad, Fahd; Uğurlu, Ekin; Abdeljawad, Thabet; Baleanu, Dumitru
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: 143
Citation - Scopus: 159
Semi-Analytical Study of Pine Wilt Disease Model With Convex Rate Under Caputo-Febrizio Fractional Order Derivative
(Pergamon-elsevier Science Ltd, 2020) Jarad, Fahd; Abdeljawad, Thabet; Shah, Kamal; Alqudah, Manar A.
In this paper, we present semi-analytical solution to Pine Wilt disease (PWD) model under the CaputoFabrizio fractional derivative (CFFD). For the proposed solution, we utilize Laplace transform coupled with Adomian decomposition method abbreviated as (LADM). The concerned method is a powerful tool to obtain semi-analytical solution for such type of nonlinear differential equations of fractional order (FODEs) involving non-singular kernel. Furthermore, we give some results for the existence of solution to the proposed model and present numerical results to verify the established analysis. (C) 2020 Elsevier Ltd. All rights reserved.
Citation - WoS: 26
Citation - Scopus: 32
On a More General Fractional Integration by Parts Formulae and Applications
(Elsevier, 2019) Gomez-Aguilar, J. F.; Jarad, Fahd; Abdeljawad, Thabet; Atangana, Abdon
The integration by part comes from the product rule of classical differentiation and integration. The concept was adapted in fractional differential and integration and has several applications in control theory. However, the formulation in fractional calculus is the classical integral of a fractional derivative of a product of a fractional derivative of a given function f and a function g. We argue that, this formulation could be done using only fractional operators: thus, we develop fractional integration by parts for fractional integrals, Riemann-Liouville, Liouville-Caputo, Caputo-Fabrizio and Atangana-Baleanu fractional derivatives. We allow the left and right fractional integrals of order alpha > 0 to act on the integrated terms instead of the usual integral and then make use of the fractional type Leibniz rules to formulate the integration by parts by means of new generalized type fractional operators with binomial coefficients defined for analytic functions. In the case alpha = 1, our formulae of fractional integration by parts results in previously obtained integration by parts in fractional calculus. The two disciplines or branches of mathematics are built differently, while classical differentiation is built with the concept of rate of change of a given function, a fractional differential operator is a convolution. (C) 2019 Elsevier B.V. All rights reserved.
Citation - WoS: 2
Citation - Scopus: 2
Hamiltonian Formulation of Singular Lagrangians on Time Scales
(Iop Publishing Ltd, 2008) Jarad, Fahd; Baleanu, Dumitru; Abdeljawad, Thabet
The Hamiltonian formulation of Lagrangian on time scale is investigated and the equivalence of Hamilton and Euler-Lagrange equations is obtained. The role of Lagrange multipliers is discussed.
Citation - WoS: 4
Citation - Scopus: 2
Locally Convex Valued Rectangular Metric Spaces and the Kannan's Fixed Point Theorem
(Eudoxus Press, Llc, 2012) Abdeljawad, Thabet; Abdeljawad, Thabet; Turkoglu, Duran; Matematik
Rectangular TVS-cone metric spaces are introduced and Kannan's fixed point theorem is proved in these spaces. Two approaches are followed for the proof. At first we prove the theorem by a direct method using the structure of the space itself. Secondly, we use the nonlinear scalarization used recently by Wei-Shih Du in [A note on cone metric fixed point theory and its equivalence, Nonlinear Analysis,72(5),2259-2261 (2010).] to prove the equivalence of the Banach contraction principle in cone metric spaces and usual metric spaces. The proof is done without any normality assumption on the cone of the locally convex topological vector space, and hence generalizing several previously obtained results.
Citation - WoS: 45
Citation - Scopus: 46
Existence of Mild Solutions To Hilfer Fractional Evolution Equations in Banach Space
(Springer Basel Ag, 2020) Abdeljawad, Thabet; Sousa, J. Vanterler da C.; Jarad, Fahd
In this paper, we investigate the existence of mild solutions to semilinear evolution fractional differential equations with non-instantaneous impulses, using the concepts of equicontinuous (alpha,beta)-resolvent operator function P-alpha,P-beta(t) and Kuratowski measure of non-compactness in Banach space Omega.
Citation - WoS: 6
Citation - Scopus: 5
Fixed Points of Generalized Contraction Mappings in Cone Metric Spaces
(Univ Osijek, dept Mathematics, 2011) Turkoglu, Duran; Abdeljawad, Thabet; Abuloha, Muhib; Abdeljawad, Thabet; Matematik
In this paper, we proved a fixed point theorem and a common fixed point theorem in cone metric spaces for generalized contraction mappings where some of the main results of Ciric in [8, 27] are recovered.
Citation - WoS: 12
Citation - Scopus: 20
Coupled Fixed Point Theorems for Partially Contractive Mappings
(Springer international Publishing Ag, 2012) Abdeljawad, Thabet
Recently, some authors have started to generalize fixed point theorems for contractive mappings in a class of generalized metric spaces in which the self-distance need not be zero. These spaces, partial metric spaces, were first introduced by Matthews in 1994. The proved fixed point theorems have been obtained for mappings satisfying contraction type conditions empty of the self-distance. In this article, we prove some coupled fixed point theorems for mappings satisfying contractive conditions allowing the appearance of self-distance terms. These partially contractive mappings do reflect the structure of the partial metric space, and hence their coupled fixed theorems generalize the previously obtained by (Aydi in Int. J. Math. Sci. 2011:Article ID 647091, 2011). Some examples are given to support our claims. MSC: 47H10, 54H25.
Citation - WoS: 1
Citation - Scopus: 1
Recent Developments and Applications on Discrete Fractional Equations and Related Topics
(Hindawi Ltd, 2013) Alzabut, Jehad; Sun, Shurong; Abdeljawad, Thabet
Citation - WoS: 32
Citation - Scopus: 52
A Generalized Q-Mittag Function by Q-Captuo Fractional Linear Equations
(Hindawi Ltd, 2012) Baleanu, Dumitru; Abdeljawad, Thabet; Benli, Betul
Some Caputo q-fractional difference equations are solved. The solutions are expressed by means of a new introduced generalized type of q-Mittag-Leffler functions. The method of successive approximation is used to obtain the solutions. The obtained q-version of Mittag-Leffler function is thought as the q-analogue of the one introduced previously by Kilbas and Saigo (1995).