Initial value problem of fractional q-differential equation with Caputo derivative
LIU Yanzhi1，YANG Yan1，DANG Yungui1,2
( 1.Department of Mathematics，Lvliang University， Lvliang 033000， Shanxi，China；2.Faculty of Mathematics and Statistics，Hubei University，Hubei Key Laboratory of Applied Mathematics，Wuhan 430062，China)
Abstract：In this paper，the initial value problem of fractional q-differential equation CDq(α)y(t)＝f(t，y(t))is considered，where α∈(0,1)∪(1,2) andCDq(α) is the Caputo q-differential operator. By using fractional Adams method with graded meshes，the predictor-corrector scheme for solving the corresponding q-Volterra integral equation is proposed，from which the numerical solution of the initial value problem is obtained and the error estimate is given. Finally，the effectiveness of this theoretical result is verified by a numerical example.
刘彦芝,杨 艳,党云贵,. Caputo型分数阶q-微分方程的初值问题[J]. 华中师范大学学报(自然科学版), 2022, 56(2): 240-244.
LIU Yanzhi,YANG Yan,DANG Yungui,. Initial value problem of fractional q-differential equation with Caputo derivative. journal1, 2022, 56(2): 240-244.
2022, Vol. 56 
