Abstract:In the present work, we have introduced a new formulation for the approximate-analytical solution of the fractional onedimensional 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.
In this paper, we consider some linear/nonlinear differential equations (DEs) containing conformable derivative operator. We obtain approximate solutions of these mentioned DEs in the form of infinite series which converges rapidly to their exact values by using and homotopy analysis method (HAM) and modified homotopy perturbation method (MHPM). Using the conformable operator in solutions of different types of DEs makes the solution steps are computable easily. Especially, the conformable operator has been used in modelling DEs and identifying particular problems such as biological, engineering, economic sciences and other some important fields of application. In this context, the aim of this study is to solve some illustrative linear/nonlinear problems as mathematically and to compare the exact solutions with the obtained solutions by considering some plots. Moreover, it is an aim to show the authenticity, applicability, and suitability of the methods constructed with the conformable operator.
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