Approximate-analytical solutions of cable equation using conformable fractional operator

Abstract

In the present work, we have introduced a new formulation for the approximate-analytical solution of the fractional one-dimensional cable differential equation (FCE) by using the conformable fractional derivative. First of all, we have redefined Adomian decomposition method (CADM) and variational iteration method (CVIM) in the conformable sense. Then, we have solved by using the mentioned methods, which can analytically solve the fractional partial differential equations (FPDEs). In order to represent the efficiencies of these proposed methods, we have compared the numerical and exact solutions of the (FCE). Also, we have found out that the proposed models defined with the conformable derivative operator are very efficient and powerful techniques in finding approximate- analytical solutions for the cable equation of fractional order. In addition, the classical derivative and integral properties are recovered partially when the fractional term (alpha) is equal to one.

Keywords

• Conformable derivative operator,approximate-analytical solution,Adomian decomposition method,variational iteration method

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