A Numerical Approach to Solve the q-Fractional Boundary Value Problems - Ying Sheng; Tie Zhang (Fractal and Fractional, 2022)
In this present paper, we study the difference method for solving a boundary value problem of the Caputo type q-fractional differential equation. This method is based on the numerical quadrature of the q-fractional derivative and the q-Taylor expansion of related function. We first derive the truncation error boundness of <semantics>O(▵<msubsup>xn2</msubsup>)</semantics>-order and prove the existence and uniqueness of the numerical solution. Then, we prove the stability of the numerical solution and give the error estimation. Numerical experiments finally verify the validity of the theoretical analysis.