An Existence Result for Some Fractional-Integro Differential Equations in Banach Spaces via Deformable Derivatives

Authors

  • Markus Mebrat
  • Gaston Mandata N'Guerekata Morgan State University

Keywords:

Deformable derivative, Krasnoselkii's theorem, \\ Weissinger's theorem, Integro-diffferential equations, mild solution

Abstract

In this paper we investigate further properties of the  deformable derivative and use the results to study        the existence of solutions to the integro-differential equation $ D^\alpha y(t)  =h(y(t))+  f(t,y(t))
+\int_{0}^{t}K(t,s,y(s))ds , t \in [0,T] $, with initial condition $y(0)=y_0, $ where $D^\alpha y(t)$ is the deformable derivative of $y$, $ 0 < \alpha < 1$.
We use Weissinger's fixed point theorem and Krasnoselkii's fixed point theorem to achieve our main results. An example is provided for illustration.

Author Biography

Gaston Mandata N'Guerekata, Morgan State University

Department of Mathematics

University Distinguished Professor

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Published

2021-11-25

Issue

Vol. 16

Section

Vol. 16, No. 8, (2022)

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