### AIMS Mathematics

2021, Issue 2: 1348-1365. doi: 10.3934/math.2021084
Research article

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

• 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.

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

### Related Papers:

• 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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• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

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