scholarly journals Semi-Analytic Technique for Solving Fractional Partial Differential Equations with Conformable Derivatives

2021 ◽  
Vol 24 (1) ◽  
pp. 39-44
Author(s):  
Noor I. Ibrahim ◽  
◽  
Osama H. Mohammed ◽  

In this work, we present a semi-analytical technique to find an approximate result of the conformable fractional partial differential equations (CFPDEs). The fractional order derivative will be in the conformable (CFD) sense. This definition is effective and simple in the solution of the fractional differential equations that have intricate solution with classical fractional derivative definition like Riemann-Liouville and Caputo. Furthermore, the result obtained by the proposed technique is like those in previous studies that used other types of approximate methods like (Homotopy analysis method) but it has the advantage of being simpler than the rest of these methods. In addition, results demonstrate obtained the Precision and effectiveness of the suggested technique.

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
A. K. Alomari

Abstract In this paper, we investigate the Sumudu transforms and homotopy analysis method (S-HAM) for solving a system of fractional partial differential equations. A general framework for solving such a kind of problems is presented. The method can also be utilized to solve systems of fractional equations of unequal orders. The algorithm is reliable and robust. Existence and convergence results concerning the proposed solution are given. Numerical examples are introduced to demonstrate the efficiency and accuracy of the algorithm.


Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 505 ◽  
Author(s):  
Rasool Shah ◽  
Hassan Khan ◽  
Poom Kumam ◽  
Muhammad Arif

The Kortweg–de Vries equations play an important role to model different physical phenomena in nature. In this research article, we have investigated the analytical solution to system of nonlinear fractional Kortweg–de Vries, partial differential equations. The Caputo operator is used to define fractional derivatives. Some illustrative examples are considered to check the validity and accuracy of the proposed method. The obtained results have shown the best agreement with the exact solution for the problems. The solution graphs are in full support to confirm the authenticity of the present method.


Sign in / Sign up

Export Citation Format

Share Document