Existence of Solution to Fractional Order Impulsive Partial Hyperbolic Differential Equations with Infinite Delay

Open Access

Original research article

Author(s):

Md. Asaduzzaman^a, Md. Zulfikar Ali^b

^aDepartment of Mathematics, Islamic University, Kushtia–7003, Bangladesh
^bDepartment of Mathematics, University of Rajshahi, Rajshahi–6205, Bangladesh

Advances in the Theory of Nonlinear Analysis and its Applications 4 (2), 77-91.

Received: November 16, 2019

Accepted: February 28, 2020

Published: March 13, 2020

Abstract

In this article, we investigate the existence of solutions to a class of initial value problems (IVPs) for fractional order impulsive partial hyperbolic differential equations (FOIPHDEs) with infinite delay. We employ the mixed Riemann–Liouville fractional derivative to construct the considered FOIPHDEs. The analysis of this article is based on the Burton–Kirk fixed point theorem. A new existence result for FOIPHDEs with infinite delay has been obtained. To support the analytical proof, an illustrative example is provided.

Keywords: FOIPHDEs, Burton–Kirk fixed point theorem.

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APA Style

Asaduzzaman, M., & Ali, M. Z. (2020). Existence of solution to fractional order impulsive partial hyperbolic differential equations with infinite delay. Advances in the Theory of Nonlinear Analysis and its Application , 4 (2), 77-91.