Shehu Conformable Fractional Transform, Theories and Applications

Year 2021, Volume: 18 Issue: 1, 24 - 32, 01.05.2021

Mohamed Elarbı Benattıa , Kacem Belghaba

Abstract

The study of famous properties of fractional derivative and their proof has gained a
lot of attention recently. In present work, we have been interested to generalizing the
definition and some rules and important properties of the Shehu transform to the conformable
fractional order which have been demonstrated. We use some properties of the
conformable fractional Shehu transform to find the general analytical solutions of linear
and nonlinear conformable fractional differential equations in the case homogeneous
and nonhomogeneous based on the new transform and Adomain polynomial method.
The two illustrative examples indicate that the used transform is powerful, effective and
applicable for the both linear and nonlinear problems.

Keywords

Shehu Conformable Transform, Fractional differential Equation, Riccati equation, Adomain polynomial

Supporting Institution

laboratoryof mathematics and its aplications

Project Number

2

Thanks

The authors are thankful to the anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper

References

• [1] S. Kazem , S. Abbasbandy, S. Kumar, “Fractional-order Legendre functions for solving fractional-order differential equations,” Applied Mathematical Modelling, vol. 37, no. 7, pp. 5498-5510, 2013.
• [2] Z. Al-Zhour, F. Alrwajeh, N. AL-MutairiI, R. ALkhaswneh, “New Results On The Conformable Fractional Sumudu Transform: Theories And Applications,” International Journal of Analysis and Applications, vol.17, no. 6, pp. 1019- 1033, 2019.
• [3] Z. Odibat, S. Momani, “Analytical comparison between the homotopy perturbation method and variational iteration method for differential equations of fractional order,” International Journal of Modern Physics, vol. 22, no. 23, pp. 4041-4058, 2008.
• [4] S. Maitama, W. Zhao, “New Integral Transform: Shehu Transform a Generlization of Sumudu and Laplace Transform For Solving Differential Equations,” International Journal of Analysis and Applications, vol. 17, no. 2, pp. 167-190, 2019.
• [5] R. Belgacem, D. Baleanu , A. Bokhari, “Shehu Transform And Applications To Caputo -Fractional Differential Equations,” International Journal of Analysis and Applications, vol. 17, no. 6 pp. 917-927, 2019.
• [6] M. Higazy, S. Aggarwal, Y. S. Hamed, “Determination of Number of Infected Cells and Concentration of Viral Particles in Plasma during HIV-1 Infections Using Shehu Transformation,” Hindawi Journal of Mathematics, doi.org/10.1155/2020/6624794, 2020. [7] A. Khalouta, A. Kadem , “A New Method to Solve Fractional Differential Equations: Inverse Fractional Shehu Transform Method,” Applications and Applied Mathematics, vol. 14, no. 2, pp. 926-941, 2019.
• [8] A. Husam H, E. Khader, “The Conformable Laplace Transform of the Fractional Chebyshev and Legendre Polynomials,”Thesis of Science in Mathematics. Zarqa University, 2017.
• [9] F. S. Silva , D. M. Moreira , M. A. Moret, “Conformable Laplace Transform of Fractional Differential Equations,” Axioms, vol. 3, no. 3, pp. 55, 2018.
• [10] Z. Odibat, S. Momani, “Modified homotopy perturbation method: application to quadratic Riccati differential equation of fractional order,” Chaos Solitons Fract, vol. 36, no. 1, pp. 167-174, 2008.