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L1-solutions of the initial value problems for implicit differential equations with Hadamard fractional derivative

Telli Benoumran, Souid Mohammed Said

Journal of Applied Analysis

2022

Vol. 28, nr 1

1--9

In this paper, we study the existence of integrable solutions for initial value problems for fractional order implicit differential equations with Hadamard fractional derivative. Our results are based on Schauder’s fixed point theorem and the Banach contraction principle fixed point theorem.

L1-solutions of the boundary value problem for implicit fractional order differentia equations

Telli Benoumran, Souid Mohammed Said

Journal of Applied Analysis

2021

Vol. 27, nr 1

121--128

The aim of this paper is to present new results on the existence of solutions for a class of the boundary value problem for fractional order implicit differential equations involving the Caputo fractional derivative. Our results are based on Schauder’s fixed point theorem and the Banach contraction principle fixed point theorem.