New class of volterra integro-differential equations with fractal-fractional operators: Existence, uniqueness and numerical scheme

Seda İğret Araz

doi:10.3934/dcdss.2021053

Article Contents

2021, Volume 14, Issue 7: 2297-2309. Doi: 10.3934/dcdss.2021053

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New class of volterra integro-differential equations with fractal-fractional operators: Existence, uniqueness and numerical scheme

Seda İğret Araz

Siirt University, Department of Mathematics Education, Siirt, Turkey

Received: June 30, 2019

Revised: November 30, 2020

Early access: May 2021

Published: July 2021

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Abstract

In this paper, we introduce a new fractional integro-differential equation involving newly introduced differential and integral operators so-called fractal-fractional derivatives and integrals. We present a numerical scheme that is convenient for obtaining solution of such equations. We give the general conditions for the existence and uniqueness of the solution of the considered equation using Banach fixed-point theorem. Both the suggested new equation and new numerical scheme will considerably contribute for our readers in theory and applications.

Keywords:

Fractal-fractional derivative,
Fractal-fractional integral,
fractional integro-differential equation,
new numerical scheme.

Mathematics Subject Classification: 26A33, 28A80, 47G20, 34A45.

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