A Local Meshless Radial Basis Functions Based Method for Solving Fractional Integral Equations

This paper presents a Localized Radial Basis Functions Collocation Method (LRBFCM) for numerically solving one and 2-dimensional Fractional Integral Equations (2D-FIEs). The LRBFCM approach decomposes the main problem into several local sub-problems of small sizes, effectively reducing the ill-conditioning of the overall problem. By employing the collocation approach and utilizing the strong form of the equation, the proposed method achieves efficiency. Additionally, the matrix operations only require the inversion of small-sized matrices, further contributing to the method's efficiency. To demonstrate the effectiveness of the LRBFCM, the paper provides test problems encompassing linear, nonlinear, Volterra, and Fredholm types of Fractional Integral Equations (FIEs). The numerical results showcase the efficiency of the proposed method, validating its performance in solving various types of FIEs.