New Results on the Conformable Fractional Sumudu Transform: Theories and Applications

Zeyad Al–Zhour ,Nouf Al-Mutairi ,Raed Alkhasawneh ,Fatimah Abdulrahman Alrawajeh

doi:10.28924/2291-8639-17-2019-1019

Abstract

In this paper, we generalize the formula of Sumudu transform to the conformable fractional order and some interesting and important rules of this transform and conformable fractional Laplace transform are derived and discussed. Moreover, we present the general analytical solution of a singular and nonlinear conformable fractional Poisson- Boltzmann differential equation based on the conformable fractional Sumudu transform. Also, our proposed method is applied successfully for obtaining the general solutions of some linear and nonhomogeneous conformable fractional differential equations. Finally, the results show that our proposed method is an efficient and can be applied for finding the general solutions of the all cases realted to the conformable fractional differential equations.

Highlights

Introduction and PreliminariesVarious types of fractional derivatives were introduced such as: Riemann-Liouville, Caputo, Modified Riemann-Liouville, Hadamard, Grunwald, Letnikov and Riesz operators
We present the general analytical solution of a singular and nonlinear conformable fractional Poisson- Boltzmann differential equation based on the conformable fractional Sumudu transform
The results show that our proposed method is an efficient and can be applied for finding the general solutions of the all cases realted to the conformable fractional differential equations

Summary

Introduction

Introduction and PreliminariesVarious types of fractional derivatives were introduced such as: Riemann-Liouville, Caputo, Modified Riemann-Liouville, Hadamard, Grunwald, Letnikov and Riesz operators. We present the general analytical solution of a singular and nonlinear conformable fractional Poisson- Boltzmann differential equation based on the conformable fractional Sumudu transform. Our proposed method is applied successfully for obtaining the general solutions of some linear and nonhomogeneous conformable fractional differential equations.

Results

Conclusion