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 Nonlinear Implicit Caputo-Hadamard Fractional Differential Equation with Fractional Boundary Conditions

Nedjemeddine Derdar

Department of Mathematics, Higher Normal School of Technological Education-Skikda, Algeria

Email address: nedjm1972@yahoo.fr

Doi : https://doi.org/10.47013/15.4.14

Cited by : Jordan J. Math & Stat., 15 (4B) (2022), 999 - 1014

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Received on: Aug. 3, 2021;                                               Accepted on: Nov. 4, 2021

 Abstract. In this paper, we establish the existence and uniqueness of solutions for a class of problem for nonlinear implicit fractional differential equations of Caputo-Hadamard type with fractional boundary conditions. The results are obtained by using Banach fixed point theorem and Schauderís fixed point theorem. An example is included to show the applicability of our results.

Keywords: Boundary value problem, CaputoHadamard fractional derivative, Implicit fractional differential equations, Fixed point theorems, Existence and uniqueness.