On study of the coupled system of nonlocal fractional q-integro-differential equations

In this paper, we introduce a coupled system of nonlocal fractional q-integro-differential equations. Under certain assumptions, we prove the existence and uniqueness of solutions for a coupled system of fractional q-integro-differential equations. We also study continuous dependence. We solve this system numerically using the finite-Simpson's and cubic spline-Simpson's methods. Finally, three examples are provided to demonstrate the efficacy of the methods employed.