Numerical Solution Of Fractional Model Of Atangana-Baleanu-Caputo Integrodifferential Equations With Integral Boundary Conditions

In this analysis, we propose an advanced numerical technique, reproducing kernel discretization method (RKDM), to investigate numerical solutions for a class of systems of fractional integro-differential equations (SFIDE) with integral boundary conditions. The Atangana-Baleanu fractional derivative is used to formulate the fractional integro-differential equations. The solution methodology is mainly based on constructing a reproducing kernel function, that satisfies the integral boundary conditions, in order to construct an orthonormal basis to formulate the solution in form of Fourier series that is uniformly convergent in the specified space W-2(2) [a, b]. Numerical applications are investigated to represent the hypothesis and to confirm the design steps of the proposed advanced technique. The numerical viewpoint indicates that the RKDM is an important tool for dealing with such issues arising in physics and engineering fields.