On the inverse problem of identifying an unknown coefficient in a space-time fractional differential equation

TL;DR

This paper introduces a fractional Taylor series method for solving inverse problems in space-time fractional differential equations, enabling precise identification of unknown coefficients without over-measured data, and demonstrating high accuracy and efficiency.

Contribution

The paper presents a novel fractional Taylor series approach for inverse problems, avoiding over-measured data and improving solution accuracy in space-time fractional differential equations.

Findings

High agreement between the method's outcomes and exact solutions

Effective implementation compared to existing methods

Accurate identification of unknown coefficients

Abstract

In this study, we focus on identifying solution and an unknown space-dependent coefficient in a space-time fractional differential equation by employing fractional Taylor series method. The substantial advantage of this method is that we don't take any over-measured data into account. Consequently, we determine the solution and unknown coefficient more precisely. The presented examples illustrate that outcomes of this method are in high agreement with the exact ones of the corresponding problem. Moreover, it can be implemented and applied effectively comparing with other methods.