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

Nasser Al-Salti; Erkinjon Karimov; Sebti Kerbal

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arXiv · 1603.09471

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

Nasser Al-Salti·Erkinjon Karimov·Sebti Kerbal

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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.

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Nasser Al-Salti, Erkinjon Karimov, Sebti Kerbal. 2016-03-31. Boundary-value problem for fractional heat equation involving Caputo-Fabrizio derivative. https://arxiv.org/abs/1603.09471

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