Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Now showing 1 - 8 of 8
  • Article
    Citation - Scopus: 5
    A Necessary and Sufficient Condition for the Existence of Periodic Solutions of Linear Impulsive Differential Equations With Distributed Delay
    (2007) Alzabut, J.O.; Alzabut, Jehad; Matematik
    A necessary and sufficient condition is established for the existence of periodic solutions of linear impulsive differential equations with distributed delay.
  • Article
    Citation - WoS: 17
    Citation - Scopus: 19
    Results on Hilfer Fractional Switched Dynamical System With Non-Instantaneous Impulses
    (indian Acad Sciences, 2022) Malik, Muslim; Baleanu, Dumitru; Kumar, Vipin
    This paper concerns with the existence, uniqueness, Ulam's Hyer (UH) stability and total controllability results for the Hilfer fractional switched impulsive systems in finite-dimensional spaces. Mainly, this paper can be divided into three parts. In the first part, we examine the existence of a unique solution. In the second part, we establish the UH stability results, and in the third part, we study the total controllability results. The main outcomes are acquired by utilising the nonlinear analysis, fractional calculus, Mittag-Leffler function and Banach contraction principle. Finally, we have given two examples to validate the obtained analytical results.
  • Article
    On Solutions of Variable-Order Fractional Differential Equations
    (Elsevier B.V., 2017) Akgül, Ali; Inc, Mustafa; Baleanu, Dumitru; Abdalla, Bahaaeldin; Jarad, Fahd; Bouchelaghem, Faycal; Abdeljawad, Thabet; Ardjouni, Abdelouaheb; Boulares, Hamid; Shah, Kamal
    Numerical calculation of the fractional integrals and derivatives is the code tosearch fractional calculus and solve fractional differential equations. The exactsolutions to fractional differential equations are compelling to get in real ap-plications, due to the nonlocality and complexity of the fractional differentialoperators, especially for variable-order fractional differential equations. There-fore, it is significant to enhance numerical methods for fractional differentialequations. In this work, we consider variable-order fractional differential equa-tions by reproducing kernel method. There has been much attention in theuse of reproducing kernels for the solutions to many problems in the recentyears. We give an example to demonstrate how efficiently our theory can beimplemented in practice.
  • Article
    Citation - Scopus: 2
    On 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 - WoS: 7
    Citation - Scopus: 6
    On a Problem for the Nonlinear Diffusion Equation With Conformable Time Derivative
    (Taylor & Francis Ltd, 2022) Baleanu, Dumitru; Zhou, Yong; Huu Can, Nguyen; Au, Vo Van
    In this paper, we study a nonlinear diffusion equation with conformable derivative: D-t((alpha)) u = Delta u = L(x, t; u(x, t)), where 0 < alpha < 1, (x, t) is an element of Omega x (0, T). We consider both of the problems: Initial value problem: the solution contains the integral I = integral(t)(0) tau(gamma) d tau (critical as gamma <= -1). Final value problem: not well-posed (if the solution exists it does not depend continuously on the given data). For the initial value problem, the lack of convergence of the integral I, for gamma <= -1. The existence for the solution is represented. For the final value problem, the Hadamard instability occurs, we propose two regularization methods to solve the nonlinear problem in case the source term is a Lipschitz function. The results of existence, uniqueness and stability of the regularized problem are obtained. We also develop some new techniques on functional analysis to propose regularity estimates of regularized solution.
  • Article
    Citation - WoS: 46
    Citation - Scopus: 47
    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.
  • Article
    Citation - WoS: 34
    Citation - Scopus: 35
    Existence and Stability Results To a Class of Fractional Random Implicit Differential Equations Involving a Generalized Hilfer Fractional Derivative
    (Amer inst Mathematical Sciences-aims, 2020) Harikrishnan, Sugumaran; Shah, Kamal; Kanagarajan, Kuppusamy; Jarad, Fahd
    In this paper, the existence, uniqueness and stability of random implicit fractional differential equations (RIFDs) with nonlocal condition and impulsive effect involving a generalized Hilfer fractional derivative (HFD) are discussed. The arguments are discussed via Krasnoselskii's fixed point theorems, Schaefer's fixed point theorems, Banach contraction principle and Ulam type stability. Some examples are included to ensure the abstract results.
  • Article
    Citation - WoS: 28
    Citation - Scopus: 33
    Existence of Periodic Solutions, Global Attractivity and Oscillation of Impulsive Delay Population Model
    (Pergamon-elsevier Science Ltd, 2007) Alzabut, J. O.; Saker, S. H.
    In this paper we consider the nonlinear impulsive delay population model. The main objective is to systematically study the qualitative behavior of the model including existence of periodic solutions, global attractivity and oscillation. The main oscillation results are the results of the prevalence of the mature cells about the periodic solutions and the global attractivity results are the conditions for nonexistence of dynamical diseases on the population. (c) 2006 Elsevier Ltd. All rights reserved.