Browsing by Author "Abdeljawad, Thabet"

Now showing 1 - 20 of 171

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.
A common fixed point theorem of a Greguš type on convex cone metric spaces
(2011) Abdeljawad, Thabet; Karapinar, Erdal; 19184; Matematik
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; 19184; Matematik
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
Citation - WoS: 6
A fite type result for sequental fractional differintial equations
(Dynamic Publishers, inc, 2010) Abdeljawad, Thabet; Abdeljawad, T.; Baleanu, Dumitru; Baleanu, D.; Jarad, Fahd; Jarad, Fahd; Mustafa, O. G.; Trujillo, J. J.; Matematik
Given the solution f of the sequential fractional differential equation aD(t)(alpha)(aD(t)(alpha) f) + P(t)f = 0, t is an element of [b, a], where -infinity < a < b < c < + infinity, alpha is an element of (1/2, 1) and P : [a, + infinity) -> [0, P-infinity], P-infinity < + infinity, is continuous. Assume that there exist t(1),t(2) is an element of [b, c] such that f(t(1)) = (aD(t)(alpha))(t(2)) = 0. Then, we establish here a positive lower bound for c - a which depends solely on alpha, P-infinity. Such a result might be useful in discussing disconjugate fractional differential equations and fractional interpolation, similarly to the case of (integer order) ordinary differential equations.
Citation - Scopus: 5
A Frational Finite Differene Inclusion
(Eudoxus Press, LLC, 2016) Baleanu, D.; Abdeljawad, Thabet; Rezapour, S.; 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.
A Gap in the Paper A Note On Cone Metric Fixed Point Theory and Its Equivalence [Nonlinear Anal. 72(5), (2010), 2259-2261]
(2011) Abdeljawad, Thabet; Karapınar, Erdal; Matematik
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.
Citation - WoS: 79
Citation - Scopus: 82
A generalized contraction principle with control functions on partial metric spaces
(Pergamon-elsevier Science Ltd, 2012) Abdeljawad, Thabet; Abdeljawad, Thabet; Karapınar, Erdal; Karapinar, Erdal; Tas, Kenan; Taş, Kenan; 19184; 4971; Matematik
Partial metric spaces were introduced by Matthews in 1994 as a part of the study of denotational semantics of data flow networks. In this article, we prove a generalized contraction principle with control functions phi and psi on partial metric spaces. The theorems we prove generalize many previously obtained results. We also give some examples showing that our theorems are indeed proper extensions. (C) 2011 Elsevier Ltd. All rights reserved.
Citation - WoS: 67
Citation - Scopus: 89
A generalized Lyapunov-type inequality in the frame of conformable derivatives
(Springeropen, 2017) Abdeljawad, Thabet; Abdeljawad, Thabet; Alzabut, Jehad; Alzabut, Jehad; Jarad, Fahd; Jarad, Fahd; 234808; Matematik
We prove a generalized Lyapunov-type inequality for a conformable boundary value problem (BVP) of order alpha is an element of (1, 2]. Indeed, it is shown that if the boundary value problem (T(alpha)(c)x)(t) + r(t) x(t) = 0, t is an element of (c, d), x(c) = x(d) = 0 has a nontrivial solution, where r is a real-valued continuous function on [c, d], then integral(d)(c) vertical bar r(t)vertical bar dt > alpha(alpha)/(alpha - 1)(alpha-1) (d - c)(a-1). (1) Moreover, a Lyapunov type inequality of the form integral(d)(c)vertical bar r(t)vertical bar dt > 3 alpha - 1/(d - c)(2 alpha-1) (3 alpha - 1/2 alpha - 1)(2 alpha-1/a), 1/2 < alpha <= 1, (2) is obtained for a sequential conformable BVP. Some examples are given and an application to conformable Sturm-Liouville eigenvalue problem is analyzed.
Citation - WoS: 54
Citation - Scopus: 56
A generalized q-fractional Gronwall inequality and its applications to nonlinear delay q-fractional difference systems
(Springeropen, 2016) Abdeljawad, Thabet; Abdeljawad, Thabet; Alzabut, Jehad; Alzabut, Jehad; Baleanu, Dumitru; Baleanu, Dumitru; Matematik
In this paper, we state and prove a new discrete q-fractional version of the Gronwall inequality. Based on this result, a particular version expressed by means of the q-Mittag-Leffler function is provided. To apply the proposed results, we prove the uniqueness and obtain an estimate for the solutions of nonlinear delay Caputo q-fractional difference system. We examine our results by providing a numerical example.
Citation - WoS: 30
Citation - Scopus: 48
A generalized q-mittag-leffler function by q-captuo fractional linear equations
(Hindawi Ltd, 2012) Abdeljawad, Thabet; Abdeljawad, Thabet; Benli, Betul; Baleanu, Dumitru; Baleanu, Dumitru; Matematik
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).
Citation - WoS: 3
Citation - Scopus: 4
A Gregus type common fixed point theorem of set-valued mappings in cone metric spaces
(Eudoxus Press, Llc, 2011) Abdeljawad, Thabet; Abdeljawad, T.; Murthy, P. P.; Taş, Kenan; Tas, K.; 4971; Matematik
The main purpose of this paper is to obtain a common fixed point theorem for a pair of set-valued mappings of Gregus type condition in cone metric spaces, so that the main result obtained in [13] will be generalized to cone metric spaces. The cone under consideration will be normal with normal constant K = 1.
Citation - WoS: 66
Citation - Scopus: 74
A Gronwall inequality via the generalized proportional fractional derivative with applications
(Springer, 2019) Alzabut, Jehad; Alzabut, Jehad; Abdeljawad, Thabet; Abdeljawad, Thabet; Jarad, Fahd; Jarad, Fahd; Sudsutad, Weerawat; 234808; Matematik
In this paper, we provide a new version for the Gronwall inequality in the frame of the generalized proportional fractional derivative. Prior to the main results, we introduce the generalized proportional fractional derivative and expose some of its features. As an application, we accommodate the newly defined derivative to prove the uniqueness and obtain a bound in terms of Mittag-Leffler function for the solutions of a nonlinear delay proportional fractional system. An example is presented to demonstrate the applicability of the theory.
Citation - WoS: 2
Citation - Scopus: 2
A NEW NUMERICAL TREATMENT FOR FRACTIONAL DIFFERENTIAL EQUATIONS BASED ON NON-DISCRETIZATION OF DATA USING LAGUERRE POLYNOMIALS
(World Scientific Publ Co Pte Ltd, 2020) Abdeljawad, Thabet; Khan, Adnan; Shah, Kamal; Jarad, Fahd; Arfan, Muhammad; Abdeljawad, Thabet; Jarad, Fahd; 234808; Matematik
In this research work, we discuss an approximation techniques for boundary value problems (BVPs) of differential equations having fractional order (FODE). We avoid the method from discretization of data by applying polynomials of Laguerre and developed some matrices of operational types for the obtained numerical solution. By applying the operational matrices, the given problem is converted to some algebraic equation which on evaluation gives the required numerical results. These equations are of Sylvester types and can be solved by using matlab. We present some testing examples to ensure the correctness of the considered techniques.
A note on the chain rule on time scales
(Çankaya Üniversitesi, 2008) Abdeljawad, Thabet; Matematik
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; Matematik
Citation - WoS: 119
Citation - Scopus: 58
A Semigroup-Like Property for Discrete Mittag-Leffler Functions
(Springeropen, 2012) Abdeljawad, Thabet; Abdeljawad, Thabet; Jarad, Fahd; Jarad, Fahd; Baleanu, Dumitru; Baleanu, Dumitru; 56389; Matematik
Discrete Mittag-Leffler function of order 0 < alpha a parts per thousand currency sign 1, , lambda not equal 1, satisfies the nabla Caputo fractional linear difference equation (C)del(alpha)(0)(t) = lambda x(t), x(0) = 1, t is an element of N-1 = {1, 2, 3, ...}. Computations can show that the semigroup identity E alpha(lambda, z1)E alpha(lambda, z2) = E alpha(lambda, z1 + z2) does not hold unless lambda = 0 or alpha = 1. In this article we develop a semigroup property for the discrete Mittag-Leffler function in the case alpha a dagger 1 is just the above identity. The obtained semigroup identity will be useful to develop an operator theory for the discrete fractional Cauchy problem with order alpha a (0, 1).
Citation - WoS: 75
Citation - Scopus: 80
A Singular Abc-Fractional Differential Equation With P-Laplacian Operator
(Pergamon-elsevier Science Ltd, 2019) Jarad, Fahd; Khan, Hasib; Jarad, Fahd; Abdeljawad, Thabet; Abdeljawad, Thabet; Khan, Aziz; 234808; Matematik
In this article, we have focused on the existence and uniqueness of solutions and Hyers-Ulam stability for ABC-fractional DEs with p-Laplacian operator involving spatial singularity. The existence and uniqueness of solutions are derived with the help of the well-known Guo-Krasnoselskii theorem. Our work is a continuation of the study carried out in the recently published article " Chaos Solitons & Fractals. 2018;117:16-20." To manifest the results, we include an example with specific parameters and assumptions. (C) 2019 Elsevier Ltd. All rights reserved.
Citation - WoS: 11
Citation - Scopus: 12
A study of boundary value problem for generalized fractional differential inclusion via endpoint theory for weak contractions
(Springer, 2020) Jarad, Fahd; Belmor, Samiha; Jarad, Fahd; Abdeljawad, Thabet; Abdeljawad, Thabet; Kilinc, Gulsen; 234808; Matematik
This note is concerned with establishing the existence of solutions to a fractional differential inclusion of a psi -Caputo-type with a nonlocal integral boundary condition. Using the concept of the endpoint theorem for phi -weak contractive maps, we investigate the existence of solutions to the proposed problem. An example is provided at the end to clarify the theoretical result.
Citation - WoS: 26
Citation - Scopus: 27
Almost periodic dynamics of a discrete Nicholson's blowflies model involving a linear harvesting term
(Springer, 2012) Alzabut, Jehad; Alzabut, Jehad; Bolat, Yasar; Abdeljawad, Thabet; Abdeljawad, Thabet; Matematik
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 - WoS: 0
Citation - Scopus: 1
Alpha fractional frequency Laplace transform through multiseries
(Springer, 2020) Abdeljawad, Thabet; Murugesan, Meganathan; Abdeljawad, Thabet; Jarad, Fahd; Gnanaprakasam, Britto Antony Xavier; Jarad, Fahd; 234808; Matematik
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.