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Algorithm For The Solution Of Nonlinear Variable-Order Pantograph Fractional Integro-Differential Equations Using Haar Method

Author

Listed:
  • KAMAL SHAH

    (Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 84428, Riyadh 11586, Saudi Arabia†Department of Mathematics, University of Malakand, Chakdara, Dir (L), Khyber Pakhtunkhwa, Pakistan)

  • ROHUL AMIN

    (��Department of Mathematics, University of Peshawar, Khyber Pakhtunkhwa, Pakistan)

  • GAUHAR ALI

    (�Department of Mathematics, Government Post Graduate Jahanzeb College Saidu Sharif Swat, Khyber Pakhtunkhwa, Pakistan)

  • NABIL MLAIKI

    (Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 84428, Riyadh 11586, Saudi Arabia)

  • THABET ABDELJAWAD

    (Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 84428, Riyadh 11586, Saudi Arabia¶Department of Medical Research, China Medical University, Taichung 40402, Taiwan)

Abstract

This research work is related to establish a powerful algorithm for the computation of numerical solution to nonlinear variable order integro-differential equations (VO-IDEs). The adopted procedure is based on the Haar Wavelet Method (HWM) to compute the required numerical solution to the proposed problem. Further, in the considered problem, a proportional-type delay term is involved, which is also known as the pantograph equation. For a physical problem to investigate the computational purposes, we need to first ensure its existence. For this purpose, we utilize classical fixed results given by Banach and Schauder to establish the sufficient conditions for existence of at least one approximate solution to the proposed problem. Two pertinent examples are given, where the error analysis is also recorded.

Suggested Citation

  • Kamal Shah & Rohul Amin & Gauhar Ali & Nabil Mlaiki & Thabet Abdeljawad, 2022. "Algorithm For The Solution Of Nonlinear Variable-Order Pantograph Fractional Integro-Differential Equations Using Haar Method," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(08), pages 1-9, December.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:08:n:s0218348x22402253
    DOI: 10.1142/S0218348X22402253
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