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Numerical Solutions of Fractional-Order Electrical RLC Circuit Equations via Three Numerical Techniques

Author

Listed:
  • Uroosa Arshad

    (Department of Mathematica, Federal Urdu University of Arts, Sciences & Technology, Karachi 75300, Pakistan)

  • Mariam Sultana

    (Department of Mathematica, Federal Urdu University of Arts, Sciences & Technology, Karachi 75300, Pakistan)

  • Ali Hasan Ali

    (Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq
    Institute of Mathematics, University of Debrecen, Pf. 400, H-4002 Debrecen, Hungary)

  • Omar Bazighifan

    (Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, 39, 00186 Roma, Italy
    Department of Mathematics, Faculty of Science, Hadhramout University, Hadhramout 50512, Yemen
    Department of Mathematics, Faculty of Education, Seiyun University, Hadhramout 50512, Yemen)

  • Areej A. Al-moneef

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Kamsing Nonlaopon

    (Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand)

Abstract

In this article, three different techniques, the Fractional Perturbation Iteration Method (FPIA), Fractional Successive Differentiation Method (FSDM), and Fractional Novel Analytical Method (FNAM), have been introduced. These three iterative methods are applied on different types of Electrical RLC-Circuit Equations of fractional-order. The fractional series approximation of the derived solutions can be established by using the obtained coefficients. These three algorithms handle the problems in a direct manner without any need for restrictive assumptions. The comparison displays an agreement between the obtained results. The beauty of this paper lies in the error analysis between the exact solution and approximate solutions obtained by these three methods which prove that the Approximate Solution obtained by FNAM converge very rapidly to the exact solution.

Suggested Citation

  • Uroosa Arshad & Mariam Sultana & Ali Hasan Ali & Omar Bazighifan & Areej A. Al-moneef & Kamsing Nonlaopon, 2022. "Numerical Solutions of Fractional-Order Electrical RLC Circuit Equations via Three Numerical Techniques," Mathematics, MDPI, vol. 10(17), pages 1-16, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3071-:d:897745
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    References listed on IDEAS

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    Cited by:

    1. Xin Liu & Lili Chen & Yanfeng Zhao, 2023. "Existence Theoremsfor Solutions of a Nonlinear Fractional-Order Coupled Delayed System via Fixed Point Theory," Mathematics, MDPI, vol. 11(7), pages 1-15, March.

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