On a higher order multi-term time-fractional partial differential equation involving Caputo-Fabrizio derivative

TL;DR

This paper studies a higher order multi-term fractional PDE with Caputo-Fabrizio derivatives, providing methods to reduce it to integer order and explicit solutions via Fourier series.

Contribution

It introduces a novel approach to solving higher order multi-term fractional PDEs with Caputo-Fabrizio derivatives, including explicit solution representation.

Findings

Reduction of fractional PDE to integer order

Explicit solutions via Fourier series

Analysis of boundary value problems for fractional heat equations

Abstract

In the present work we discuss higher order multi-term partial differential equation (PDE) with the Caputo-Fabrizio fractional derivative in time. We investigate a boundary value problem for fractional heat equation involving higher order Caputo-Fabrizio derivatives in time-variable. Using method of separation of variables and integration by parts, we reduce fractional order PDE to the integer order. We represent explicit solution of formulated problem in particular case by Fourier series.