Browsing by Author "Abdeljawad, T."

Now showing 1 - 17 of 17

Citation - WoS: 6
A fite type result for sequental fractional differintial equations
(Dynamic Publishers, inc, 2010) Abdeljawad, T.; Baleanu, D.; 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 - 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, T.; Murthy, P. P.; 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 - Scopus: 3
A special issue:Recent developments in nonlinear partial differential equations
(Erdal Karapinar, 2020) Abdeljawad, T.; Al-Mdallal, Q.M.; Hammouch, Z.; Jarad, F.; F.; Matematik
Citation - WoS: 20
Citation - Scopus: 18
Banach contraction principle for cyclical mappings on partial metric spaces
(Springer international Publishing Ag, 2012) Abdeljawad, T.; Alzabut, J. O.; Mukheimer, A.; Zaidan, Y.; Matematik
We prove that the Banacah contraction principle proved by Matthews in 1994 on 0-complete partial metric spaces can be extended to cyclical mappings. However, the generalized contraction principle proved by (Ilic et al. in Appl. Math. Lett. 24:1326-1330, 2011) on complete partial metric spaces can not be extended for cyclical mappings. Some examples are given to illustrate our results. Moreover, our results generalize some of the results obtained by (Kirk et al. in Fixed Point Theory 4(1):79-89, 2003). An Edelstein type theorem is also extended when one of the sets in the cyclic decomposition is 0-compact.
Citation - WoS: 17
Citation - Scopus: 13
Best proximity points for cyclical contraction mappings with 0-boundedly compact decompositions
(Eudoxus Press, Llc, 2013) Abdeljawad, T.; Alzabut, J. O.; 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 - Scopus: 50
Development of TOPSIS Technique under Pythagorean Fuzzy Hypersoft Environment Based on Correlation Coefficient and Its Application towards the Selection of Antivirus Mask in COVID-19 Pandemic
(Hindawi Limited, 2021) Zulqarnain, R.M.; Siddique, I.; Jarad, F.; Ali, R.; Abdeljawad, T.; 234808; Matematik
The correlation coefficient between two variables plays an important role in statistics. Also, the accuracy of relevance assessment depends on information from a set of discourses. The data collected from numerous statistical studies are full of exceptions. The Pythagorean fuzzy hypersoft set (PFHSS) is a parameterized family that deals with the subattributes of the parameters and an appropriate extension of the Pythagorean fuzzy soft set. It is also the generalization of the intuitionistic fuzzy hypersoft set (IFHSS), which is used to accurately assess insufficiency, anxiety, and uncertainties in decision-making. The PFHSS can accommodate more uncertainties compared to the IFHSS, and it is the most substantial methodology to describe fuzzy information in the decision-making process. The core objective of the this study is to develop the notion and features of the correlation coefficient and the weighted correlation coefficient for PFHSS and to introduce the aggregation operators such as Pythagorean fuzzy hypersoft weighted average (PFHSWA) and Pythagorean fuzzy hypersoft weighted geometric (PFHSWG) operators under the PFHSS scenario. A prioritization technique for order preference by similarity to the ideal solution (TOPSIS) under PFHSS based on correlation coefficients and weighted correlation coefficients is presented. Through the developed methodology, a technique for solving multiattribute group decision-making (MAGDM) problem is planned. Also, the importance of the developed methodology and its application in indicating multipurpose antivirus mask throughout the COVID-19 pandemic period is presented. A brief comparative analysis is described with the advantages, effectiveness, and flexibility of numerous existing studies that demonstrate the effectiveness of the proposed method. © 2021 Rana Muhammad Zulqarnain et al.
Citation - WoS: 197
Citation - Scopus: 192
Existence and uniqueness of a common fixed point on partial metric spaces
(Pergamon-elsevier Science Ltd, 2011) Abdeljawad, T.; Karapinar, E.; Tas, K.; 19184; 4971; Matematik
In this work, a general form of the weak phi-contraction is considered on partial metric spaces, to get a common fixed point. It is shown that self-mappings S, T on a complete partial metric space X have a common fixed point if it is a generalized weak phi-contraction. (C) 2011 Elsevier Ltd. All rights reserved.
Existence of Solutions of Multi-Order Fractional Differential Equations
(Elsevier B.V., 2025) Bouchelaghem, F.; Boulares, H.; Ardjouni, A.; Jarad, F.; Abdeljawad, T.; Abdalla, B.; Shah, K.; Matematik
Recently, the field of fractional calculus has garnered significant attention due to its wide range of applications across various disciplines in science and engineering. Numerous results have been derived using tools from numerical functional analysis and fixed point theory to address a variety of problems in this area. This study employs the Banach Fixed Point Theorem (BFPT) to establish the existence and uniqueness of solutions for Riemann–Liouville fractional differential equations (RLFDEs) involving multiple orders. Sufficient conditions for the existence of solutions to the problem under consideration have been provided. Furthermore, an illustrative example is presented to validate the theoretical findings. © 2025
Citation - Scopus: 50
Nonlinear delay fractional difference equations with applications on discrete fractional lotka–volterra competition model
(Eudoxus Press, LLC, 2018) Alzabut, J.; Abdeljawad, T.; Baleanu, D.; 56389; Matematik
The existence and uniqueness of solutions for nonlinear delay fractional difference equations are investigated in this paper. We prove the main results by employing the theorems of Krasnoselskii’s Fixed Point and Arzela–Ascoli. As an application of the main theorem, we provide an existence result on the discrete fractional Lotka–Volterra model. ©2018 by Eudoxus Press, LLC. All rights reserved.
Citation - Scopus: 2
On abstract Cauchy problems in the frame of a generalized Caputo type derivative
(DergiPark, 2023) Bourchi, S.; Jarad, F.; Adjabi, Y.; Abdeljawad, T.; Mahariq, I.; 234808; Matematik
In this paper, we consider a class of abstract Cauchy problems in the framework of a generalized Caputo type fractional. We discuss the existence and uniqueness of mild solutions to such a class of fractional differential equations by using properties found in the related fractional calculus, the theory of uniformly continuous semigroups of operators and the fixed point theorem. Moreover, we discuss the continuous dependence on parameters and Ulam stability of the mild solutions. At the end of this paper, we bring forth some examples to endorse the obtained results. © 2023, DergiPark. All rights reserved.
Citation - WoS: 117
Citation - Scopus: 121
On Cauchy problems with Caputo Hadamard fractional derivatives
(Eudoxus Press, Llc, 2016) Adjabi, Y.; Jarad, Fahd; Baleanu, D.; Abdeljawad, T.; 234808; Matematik
The current work is motivated by the so-called Caputo-type modification of the Hadamard or Caputo Hadamard fractional derivative discussed in [4]. The main aim of this paper is to study Cauchy problems for a differential equation with a left Caputo Hadamard fractional derivative in spaces of continuously differentiable functions. The equivalence of this problem to a nonlinear Volterra type integral equation of the second kind is shown. On the basis of the obtained results, the existence and uniqueness of the solution to the considered Cauchy problem is proved by using Banach's fixed point theorem. Finally, two examples are provided to explain the applications of the results.
Citation - WoS: 15
Citation - Scopus: 15
On fractional differential inclusion problems involving fractional order derivative with respect to another function
(World Scientific Publ Co Pte Ltd, 2020) Belmor, Samiha; Jarad, F.; Abdeljawad, T.; Alqudah, Manar A.; 234808; Matematik
In this research work, we investigate the existence of solutions for a class of nonlinear boundary value problems for fractional-order differential inclusion with respect to another function. Endpoint theorem for phi-weak contractive maps is the main tool in determining our results. An example is presented in aim to illustrate the results.
Citation - Scopus: 3
On Mittag-Leffler Kernel-Dependent Fractional Operators with Variable Order
(Springer International Publishing, 2019) Bahaa, G.M.; Abdeljawad, T.; Jarad, F.; 234808; Matematik
In this work, integration by parts formulas for variable-order fractional operators with Mittag-Leffler kernels are presented and applied to study constrained fractional variational principles involving variable-order Caputo-type Atangana–Baleanu’s derivatives, where the variable-order fractional Euler–Lagrange equations are investigated. A general formulation of fractional Optimal Control Problems (FOCPs) and a solution scheme for such class of systems are proposed. The performance index of a FOCP is taken into consideration as function of state as well as control variables. © 2019, Springer Nature Singapore Pte Ltd.
Citation - WoS: 82
Citation - Scopus: 84
On the weighted fractional operators of a function with respect to another function
(World Scientific Publ Co Pte Ltd, 2020) Jarad, F.; Abdeljawad, T.; Shah, K.; 234808; Matematik
The primary goal of this study is to define the weighted fractional operators on some spaces. We first prove that the weighted integrals are bounded in certain spaces. Afterwards, we discuss the weighted fractional derivatives defined on absolute continuous-like spaces. At the end, we present a modified Laplace transform that can be applied perfectly to such operators.
Citation - WoS: 7
Citation - Scopus: 6
Perron's theorem for q-delay difference equations
(Natural Sciences Publishing Corp-nsp, 2011) Alzabut, J. O.; Abdeljawad, T.; 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: 2
Citation - Scopus: 4
Some fixed point results in tvs-cone metric spaces
(House Book Science-casa Cartii Stiinta, 2013) Abdeljawad, T.; Rezapour, Sh; Matematik
Every TVS-cone metric space is topologically isomorphic to a topological metric space. In this paper, by using a nonlinear scalarization, we give some fixed point results with nonlinear contractive conditions on TVS-cone metric spaces.
Citation - Scopus: 1
Some properties for certain subclasses of analytic functions associated with k−integral operators
(Erdal Karapinar, 2020) Abujarad, E.S.A.; Abujarad, M.H.A.; Abdeljawad, T.; Jarad, F.; 234808; Matematik
In this paper, the k-integral operators for analytic functions defined in the open unit disc U = {z ∈ C: |z| < 1} are introduced. Several new subclasses of analytic functions satisfying certain relations involving these operators are also introduced. Further, we establish the inclusion relation for these subclasses. Next, the integral preserving properties of a k-integral operator satisfied by these newly introduced subclasses are obtained. Some applications of the results are discussed. Concluding remarks are also given. © 2020, Erdal Karapinar. All rights reserved.