On nonlocal boundary value problems of nonlinear nth-order q-difference equations

In this paper, we study the existence and uniqueness of the solution of nonlocal boundary value problems of nonlinear nth-order q-difference equations. The uniqueness follows from the well-known Banach contraction principle. We prove that those q-solutions, under some conditions, converge to the classical solution when q approaches 1(-). A new numerical algorithm is introduced via definition of q-calculus for solving the nonlocal boundary value problem of nonlinear nth-order q-difference equations. The numerical experiments show that the algorithm is quite accurate and efficient. Moreover, numerical results are carried out to confirm the accuracy of our theoretical results of the algorithm.