Existence and stability results for a nonlinear implicit fractional differential equation with a discrete delay

Open Access

Original research article

Author(s):

Rahima Atmania

LMA lab., Department of Mathematics, Badji Mokhtar University of Annaba, Annaba 23000, Algeria.

Advances in the Theory of Nonlinear Analysis and its Applications 6(2), 246-257.

Received: January 5, 2022

Accepted: February 23, 2022

Published: February 25, 2022

Abstract

In this paper, we are concerned with a class of nonlinear implicit fractional differential equation with a discrete delay. By means of the contraction mapping principle, we prove the existence of a unique solution. Then, we investigate the continuous dependence of the solution upon the initial delay data and the Ulam stability.

Keywords: Fractional differential equation, discrete delay, existence and continuous dependence of solution on initial data, Ulam stability, Banach fixed point theorem.

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APA Style

Atmania, R. (2022). Existence and stability results for a nonlinear implicit fractional differential equation with a discrete delay. Advances in the Theory of Nonlinear Analysis and its Application, 6(2), 246-257.