Mathematical Analysis of Coupled System with Non Local Coupled Integral Boundary Conditions

This work is devoted to study a class of fractional order coupled system with nonlocal coupled Integral Boundary Conditions (IBCs). We use Conformable Fractional Order Derivative (CFOD) to investigate the mentioned problem for existence theory, stability and numerical analysis. The CFOD has some useful features as compared to other kinds of fractional order operators like satisfying product, quotient and chain rules which help in computational analysis. On the use of fixed point theorems combined with the tools of nonlinear functional analysis, appropriate results are deduced for existence, uniqueness and stability of solution. The concept introduced by Ulam-Hyers (U-H) is used to derive some results for stability theory. In addition, numerical tool based on Runge-Kutta method of order four (RK4) is used to compute approximate solution to the considered problem. We present two examples for verification of our results. Also, we present the graphical illustrations for various fractional orders of the two considered examples.