Boundary-value problems for fractional heat equation involving Caputo-Fabrizio derivative

Year 2016, Volume: 4 Issue: 4, 79 - 89, 31.12.2016

Nasser Al-salti Erkinjon Karimov , Sebti Kerbal

Abstract

In this work, we consider a number of boundary-value
problems for time-fractional heat equation with the recently introduced
Caputo-Fabrizio derivative. Using the method of separation of variables, we
prove a unique solvability of the stated problems. Moreover, we have found an
explicit solution to certain initial value problem for Caputo-Fabrizio
fractional order differential equation by reducing the problem to a Volterra
integral equation. Different forms of solution were presented depending on the
values of the parameter appeared in the problem.

Keywords

Caputo-Fabrizio fractional derivative

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