An Efficient Analytical Approach for the Solution of Certain Fractional-Order Dynamical Systems

Ya Qin, Adnan Khan, Izaz Ali, Maysaa Al Qurashi, Hassan Khan, Rasool Shah and Dumitru Baleanu
Additional contact information
Ya Qin: Data Recovery Lab of Sichuan Province, Neijiang Normal University, Neijiang 641112, China
Adnan Khan: Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan
Izaz Ali: Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan
Maysaa Al Qurashi: Department of Mathematics, King Saud University, Riyadh 11495, Saudi Arabia
Hassan Khan: Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan
Rasool Shah: Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan
Dumitru Baleanu: Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey

Energies, 2020, vol. 13, issue 11, 1-14

Abstract: Mostly, it is very difficult to obtained the exact solution of fractional-order partial differential equations. However, semi-analytical or numerical methods are considered to be an alternative to handle the solutions of such complicated problems. To extend this idea, we used semi-analytical procedures which are mixtures of Laplace transform, Shehu transform and Homotopy perturbation techniques to solve certain systems with Caputo derivative differential equations. The effectiveness of the present technique is justified by taking some examples. The graphical representation of the obtained results have confirmed the significant association between the actual and derived solutions. It is also shown that the suggested method provides a higher rate of convergence with a very small number of calculations. The problems with derivatives of fractional-order are also solved by using the present method. The convergence behavior of the fractional-order solutions to an integer-order solution is observed. The convergence phenomena described a very broad concept of the physical problems. Due to simple and useful implementation, the current methods can be used to solve problems containing the derivative of a fractional-order.

Keywords: Homotory perturbation method; Shehu transform; Burger equation; Caputo operator (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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