Continuity of solutions of a class of fractional equations

TL;DR

This paper investigates how solutions to certain fractional differential equations change continuously when fractional parameters or initial conditions vary, which is crucial for accurate modeling in applied sciences.

Contribution

It establishes the continuity of solutions for a class of fractional equations, including Abel and time fractional diffusion equations, with respect to parameters and initial values.

Findings

Solutions depend continuously on fractional parameters.

Continuity holds for initial value variations.

Applicable to Abel and fractional diffusion equations.

Abstract

In practice many problems related to space/time fractional equations depend on fractional parameters. But these fractional parameters are not known a priori in modelling problems. Hence continuity of the solutions with respect to these parameters is important for modelling purposes. In this paper we will study the continuity of the solutions of a class of equations including the Abel equations of the first and second kind, and time fractional diffusion type equations. We consider continuity with respect to the fractional parameters as well as the initial value.