New iterative approach for the solutions of fractional order inhomogeneous partial differential equations

Laiq Zada; Rashid Nawaz; Sumbal Ahsan; Kottakkaran Sooppy Nisar; Dumitru Baleanu; Laiq Zada; Rashid Nawaz; Sumbal Ahsan; Kottakkaran Sooppy Nisar; Dumitru Baleanu

doi:10.3934/math.2021084

AIMS Mathematics

2021, Volume 6, Issue 2: 1348-1365. doi: 10.3934/math.2021084

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Research article

New iterative approach for the solutions of fractional order inhomogeneous partial differential equations

1.
Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa, Pakistan
2.
Department of Mathematics, College of Arts and Sciences, Wadi Aldawaser, 11991, Prince Sattam bin Abdulaziz University, Saudi Arabia
3.
Department of Mathematics, Cankaya University, Ankara 06790, Turkey
4.
Institute of Space Sciences, 077125 Magurele-Bucharest, Romania
5.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40447, Taiwan

Received: 17 August 2020 Accepted: 29 October 2020 Published: 18 November 2020
MSC : 11J20, 32W50, 39B12

In this paper, the study of fractional order partial differential equations is made by using the reliable algorithm of the new iterative method (NIM). The fractional derivatives are considered in the Caputo sense whose order belongs to the closed interval [0, 1]. The proposed method is directly extended to study the fractional-order Roseau-Hyman and fractional order inhomogeneous partial differential equations without any transformation to convert the given problem into integer order. The obtained results are compared with those obtained by Variational Iteration Method (VIM), Homotopy Perturbation Method (HPM), Laplace Variational Iteration Method (LVIM) and the Laplace Adominan Decomposition Method (LADM). The results obtained by NIM, show higher accuracy than HPM, LVIM and LADM. The accuracy of the proposed method improves by taking more iterations.
- fractional order Roseau-Hyman equation,
- fractional order inhomogeneous system,
- fractional calculus,
- new iterative method,
- approximate solutions
Citation: Laiq Zada, Rashid Nawaz, Sumbal Ahsan, Kottakkaran Sooppy Nisar, Dumitru Baleanu. New iterative approach for the solutions of fractional order inhomogeneous partial differential equations[J]. AIMS Mathematics, 2021, 6(2): 1348-1365. doi: 10.3934/math.2021084

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Abstract

In this paper, the study of fractional order partial differential equations is made by using the reliable algorithm of the new iterative method (NIM). The fractional derivatives are considered in the Caputo sense whose order belongs to the closed interval [0, 1]. The proposed method is directly extended to study the fractional-order Roseau-Hyman and fractional order inhomogeneous partial differential equations without any transformation to convert the given problem into integer order. The obtained results are compared with those obtained by Variational Iteration Method (VIM), Homotopy Perturbation Method (HPM), Laplace Variational Iteration Method (LVIM) and the Laplace Adominan Decomposition Method (LADM). The results obtained by NIM, show higher accuracy than HPM, LVIM and LADM. The accuracy of the proposed method improves by taking more iterations.

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