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Theoretical And Computational Results For Mixed Type Volterra–Fredholm Fractional Integral Equations

Author

Listed:
  • ROHUL AMIN

    (Department of Mathematics, University of Peshawar, Khyber Pakhtunkhwa 25120, Pakistan)

  • HUSSAM ALRABAIAH

    (Department of Mathematics, Tafila Technical University, Tafila, Jordan3College of Engineering, Al Ain University, Al Ain, UAE)

  • IBRAHIM MAHARIQ

    (College of Engineering and Technology, American University of the Middle East, Kuwait)

  • ANWAR ZEB

    (Department of Mathematics, COMSATS University Islamabad, Abbotabad Campus, Khyber Pakhtunkhawa, Pakistan)

Abstract

In this paper, we develop a numerical method for the solutions of mixed type Volterra–Fredholm fractional integral equations (FIEs). The proposed algorithm is based on Haar wavelet collocation technique (HWCT). Under certain conditions, we prove the existence and uniqueness of the solution. Also, some stability results are given of Hyers–Ulam (H–U) type. With the help of the HWCT, the considered problem is transformed into a system of algebraic equations which is then solved for the required results by using Gauss elimination algorithm. Some numerical examples for convergence of the proposed technique are taken from the literature. Maximum absolute and root mean square errors are calculated for different collocation points (CPs). The results show that the HWCT is an effective method for solving FIEs. The convergence rate for different CPS is also calculated, which is nearly equal to 2.

Suggested Citation

  • Rohul Amin & Hussam Alrabaiah & Ibrahim Mahariq & Anwar Zeb, 2022. "Theoretical And Computational Results For Mixed Type Volterra–Fredholm Fractional Integral Equations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-9, February.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:01:n:s0218348x22400357
    DOI: 10.1142/S0218348X22400357
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