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Solving nonlinear systems of fractional-order partial differential equations using an optimization technique based on generalized polynomials

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Abstract

This paper addresses the application of generalized polynomials for solving nonlinear systems of fractional-order partial differential equations with initial conditions. First, the solutions are expanded by means of generalized polynomials through an operational matrix. The unknown free coefficients and control parameters of the expansion with generalized polynomials are evaluated by means of an optimization process relating the nonlinear systems of fractional-order partial differential equations with the initial conditions. Then, the Lagrange multipliers are adopted for converting the problem into a system of algebraic equations. The convergence of the proposed method is analyzed. Several prototype problems show the applicability of the algorithm. The approximations obtained by other techniques are also tested confirming the high accuracy and computational efficiency of the proposed approach.

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Authors and Affiliations

  1. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    H. Hassani

  2. Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, R. Dr. António Bernardino de Almeida 413, 4249-015, Porto, Portugal

    J. A. Tenreiro Machado

  3. Department of Mathematics, Yasouj University, Yasouj, Iran

    E. Naraghirad

  4. Department of Computer Engineering, Payame Noor University, Tehran, Iran

    B. Sadeghi

Authors
  1. H. Hassani
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  2. J. A. Tenreiro Machado
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  3. E. Naraghirad
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  4. B. Sadeghi
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Correspondence to H. Hassani.

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Communicated by Agnieszka Malinowska.

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Hassani, H., Machado, J.A.T., Naraghirad, E. et al. Solving nonlinear systems of fractional-order partial differential equations using an optimization technique based on generalized polynomials. Comp. Appl. Math. 39, 300 (2020). https://doi.org/10.1007/s40314-020-01362-w

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  • DOI: https://doi.org/10.1007/s40314-020-01362-w

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