Density-Dependent Conformable Space-time Fractional Diffusion-Reaction Equation and Its Exact Solutions

Abstract

Abstract In this article, a special type of fractional differential equations (FDEs) named the density-dependent conformable fractional diffusion-reaction (DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>exp</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mo>−</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>ε</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">)</mml:mo> </mml:math> -expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.