Chebyshev Polynomials of the First Kind for Solving a Novel Fractional Inverse Problems

Abstract

This research investigates an inverse problem related to a fractional partial differential equation of order α ∈(0 , 2]. This equation is connected to a differential equation defined by Chebyshev polynomials of the first kind. We start by establishing the existence and uniqueness of solutions for the given fractional evolution equation. Utilizing the first kind of Chebyshev polynomials as a basis, we derive the solutions through a series expansion and examine its convergence.