Abstract
In this article, the approximate analytical solutions of four different types of conformable partial differential equations are investigated. First, the conformable Laplace transform homotopy perturbation method is reformulated. Then, the approximate analytical solution of four types of conformable partial differential equations is presented via the proposed technique. To check the accuracy of the proposed technique, the numerical and exact solutions are compared with each other. From this comparison, we conclude that the proposed technique is very efficient and easy to apply to various types of conformable partial differential equations.
Highlights
Khalil et al suggested recently an alternative fractional derivative of local type, named as conformable derivative [3] to solve some issues concerning the challenge of solving fractional differential equations (F-DEs) of nonlocal type
A new numerical technique that is relied on the homotopy perturbation method (HPM) and Laplace transform (LT) has been proposed in [8] to solve F-DEs
Fall et al [11] implemented the homotopy perturbation method to obtain the analytical solution of time-fractional Black–Scholes (T-Black–Scholes equation (BSEs)) and the generalized fractional BSEs
Summary
Khalil et al suggested recently an alternative fractional derivative of local type, named as conformable derivative [3] to solve some issues concerning the challenge of solving fractional differential equations (F-DEs) of nonlocal type. In [10], LTHPM is discussed to obtain the approximate analytical solution of space-fractional and time-fractional Burgers equations. Ey obtained an approximate analytical solution to these equations.
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