THEORETICAL AND COMPUTATIONAL RESULTS FOR MIXED TYPE VOLTERRA–FREDHOLM FRACTIONAL INTEGRAL EQUATIONS

Rohul Amin (), Hussam Alrabaiah, Ibrahim Mahariq () and Anwar Zeb ()
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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

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-9

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.

Keywords: FIEs; Volterra–Fredholm Integral Equations; Existence Result; HWCT; CPs (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22400357

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