Solving PDEs of fractional order using the unified transform method

TL;DR

This paper extends the unified transform method, also known as the Fokas method, to efficiently solve a broad class of fractional order partial differential equations, demonstrating its practical applicability.

Contribution

The paper adapts and modifies the Fokas method to handle fractional PDEs, expanding its scope and demonstrating its effectiveness on a model problem.

Findings

Successfully applied the method to a fractional PDE model

Showed the method's adaptability to fractional order equations

Provided a framework for solving various fractional PDEs

Abstract

We consider the unified transform method, also known as the Fokas method, for solving partial differential equations. We adapt and modify the methodology, incorporating new ideas where necessary, in order to apply it to solve a large class of partial differential equations of fractional order. We demonstrate the applicability of the method by implementing it to solve a model fractional problem.