On the analytical and numerical study for fractional q -integrodifferential equations

In this paper, we give some basic concepts of q -calculus that will be needed in this paper. Then, we built the q-nonlocal condition that ensures the solution existence and uniqueness of the fractional q-integrodifferential equation. Also, we introduce the continuous dependence of the solution. We find the numerical solution using the finite-difference-Trapezoidal and the cubic B-spline-Trapezoidal methods. Finally, we give three examples to illustrate the validity of our main results.