Existence results of self-similar solutions to the Caputo-type's space-fractional heat equation

Abstract

This paper investigates the problem of existence and uniqueness of solutions under the self-similar forms to the space-fractional heat equation. By applying the properties of Banach's fixed point theorems, Schauder's fixed point theorem and the nonlinear alternative of Leray-Schauder type, we establish several results on the existence and uniqueness of self-similar solutions to this equation.

Keywords

• space-fractional heat equation
• self-similar solutions
• existence
• uniqueness