Open AccessTHEORETICAL AND COMPUTATIONAL RESULTS FOR MIXED TYPE VOLTERRA–FREDHOLM FRACTIONAL INTEGRAL EQUATIONS
Author(s) -
Rohul Amin,
Hussam Alrabaiah,
İbrahim Mahariq,
Anwar Zeb
Publication year - 2021
Publication title -
fractals
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.654
H-Index - 44
eISSN - 1793-6543
pISSN - 0218-348X
DOI - 10.1142/s0218348x22400357
Subject(s) - mathematics , uniqueness , convergence (economics) , collocation method , type (biology) , integral equation , stability (learning theory) , algebraic equation , fredholm integral equation , mathematical analysis , collocation (remote sensing) , nonlinear system , computer science , differential equation , ordinary differential equation , ecology , physics , quantum mechanics , machine learning , economics , biology , economic growth
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 [Formula: see text].