TY - JOUR
T1 - A distinct numerical approach for the solution of some kind of initial value problem involving nonlinear q-fractional differential equations
TT - رویکرد عددی متمایز در جواب نوعی از مسئله مقدار اولیه شامل معادلات دیفرانسیل q-کسری غیرخطی
JF - khu-mmr
JO - khu-mmr
VL - 8
IS - 3
UR - http://mmr.khu.ac.ir/article-1-3103-en.html
Y1 - 2022
SP - 116
EP - 91
KW - The fractional q-derivativeو Difference formulaو Truncation errorوUnconditional Stabilityو The q-fractional differential equationو Convergence analysis.
N2 - The fractional calculus deals with the generalization of integration and differentiation of integer order to those ones of any order. The q-fractional differential equation usually describe the physical process imposed on the time scale set Tq. In this paper, we first propose a difference formula for discretizing the fractional q-derivative of Caputo type with order and scale index . We establish a rigorous truncation error boundness and prove that this difference formula is unconditionally stable. Then, we consider the difference method for solving the initial problem of q-fractional differential equation: . We prove the unique existence and stability of the difference solution and give the convergence analysis. Numerical experiments show the effectiveness and high accuracy of the proposed difference method.
M3
ER -