Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
Browse
16 results
Search Results
Article Citation - WoS: 51Citation - Scopus: 66Existence and Uniqueness of Solutions to Fractional Differential Equations in the Frame of Generalized Caputo Fractional Derivatives(Springer, 2018) Gambo, Y. Y.; Ameen, R.; Jarad, Fahd; Abdeljawad, T.The generalized Caputo fractional derivative is a name attributed to the Caputo version of the generalized fractional derivative introduced in Jarad et al. (J. Nonlinear Sci. Appl. 10:2607-2619, 2017). Depending on the value of. in the limiting case, the generality of the derivative is that it gives birth to two different fractional derivatives. However, the existence and uniqueness of solutions to fractional differential equations with generalized Caputo fractional derivatives have not been proven. In this paper, Cauchy problems for differential equations with the above derivative in the space of continuously differentiable functions are studied. Nonlinear Volterra type integral equations of the second kind corresponding to the Cauchy problem are presented. Using Banach fixed point theorem, the existence and uniqueness of solution to the considered Cauchy problem is proven based on the results obtained.Article Citation - WoS: 2Citation - Scopus: 5Some Fixed Point Results in Tvs-Cone Metric Spaces(House Book Science-casa Cartii Stiinta, 2013) Abdeljawad, T.; Abdeljawad, Thabet; Rezapour, Sh; MatematikEvery 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.Article Citation - WoS: 121Citation - Scopus: 125On Cauchy Problems With Caputo Hadamard Fractional Derivatives(Eudoxus Press, Llc, 2016) Jarad, Fahd; Adjabi, Y.; Baleanu, Dumitru; Jarad, Fahd; Baleanu, D.; Abdeljawad, Thabet; Abdeljawad, T.; MatematikThe 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.Article Citation - WoS: 7Citation - Scopus: 6Perron's Theorem for Q-Delay Difference Equations(Natural Sciences Publishing Corp-nsp, 2011) Alzabut, Jehad; Alzabut, J. O.; Abdeljawad, T.; Abdeljawad, Thabet; MatematikIn this paper, we prove that if a linear q-delay difference equation satisfies Perron's condition then its trivial solution is uniformly asymptotically stable.Article Citation - Scopus: 55Nonlinear Delay Fractional Difference Equations With Applications on Discrete Fractional Lotka–volterra Competition Model(Eudoxus Press, LLC, 2018) Abdeljawad, Thabet; Alzabut, J.; Abdeljawad, T.; Baleanu, Dumitru; Baleanu, D.; MatematikThe 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.Article Citation - WoS: 6A Fite Type Result for Sequential Fractional Differential Equations(Dynamic Publishers, inc, 2010) Abdeljawad, Thabet; Abdeljawad, T.; Baleanu, Dumitru; Baleanu, D.; Jarad, Fahd; Jarad, Fahd; Mustafa, O. G.; Trujillo, J. J.; MatematikGiven 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.Article Citation - WoS: 17Citation - Scopus: 13Best 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.; MatematikThe 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.Article Citation - Scopus: 2On Abstract Cauchy Problems in the Frame of a Generalized Caputo Type Derivative(DergiPark, 2023) Adjabi, Y.; Abdeljawad, T.; Mahariq, I.; Bourchi, S.; Jarad, F.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.Article Citation - Scopus: 1Some Properties for Certain Subclasses of Analytic Functions Associated With K−integral Operators(Erdal Karapinar, 2020) Abdeljawad, T.; Jarad, F.; Abujarad, E.S.A.; Abujarad, M.H.A.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.Article Citation - WoS: 103Citation - Scopus: 104On the Weighted Fractional Operators of a Function With Respect To Another Function(World Scientific Publ Co Pte Ltd, 2020) Shah, K.; Jarad, F.; Abdeljawad, T.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.