A NEW TECHNIQUE FOR APPROXIMATE SOLUTION OF FRACTIONAL-ORDER PARTIAL DIFFERENTIAL EQUATIONS

Laiq Zada (), Rashid Nawaz (), Mohammad A. Alqudah () and Kottakkaran Sooppy Nisar
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Laiq Zada: Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa, Pakistan
Rashid Nawaz: Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa, Pakistan
Mohammad A. Alqudah: ��Department of Basic Sciences, School of Basic Sciences and Humanities, German Jordanian University Amman 11180, Jordan
Kottakkaran Sooppy Nisar: ��Department of Mathematics, College of Arts and Sciences, Wadi Adawaser, Prince Sattam bin Abdulaziz University, Saudi Arabia

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-8

Abstract: In the present paper, the optimal auxiliary function method (OAFM) has been extended for the first time to fractional-order partial differential equations (FPDEs) with convergence analysis. To find the accuracy of the OAFM, we consider the fractional-order KDV-Burger and fifth-order Sawada–Kotera equations as a test example. The proposed technique has auxiliary functions and convergence control parameters, which accelerate the convergence of the method. The other advantage of this method is that there is no need for a small or large parameter assumption, and it gives an approximate solution after only one iteration. Further, the obtained results have been compared with the exact solution through different graphs and tables, which shows that the proposed method is very effective and easy to implement for different FPDEs.

Keywords: Optimal Auxiliary Function Method; Fractional Calculus; Fractional Nonlinear KDV-Burgers; Fifth-Order Sawada–Kotera Equation (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22400151

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