%0 Journal Article
%A فتحی پور, اعظم
%A fathipour, azam
%T A distinct numerical approach for the solution of some kind of initial value problem involving nonlinear q-fractional differential equations
%J Mathematical Researches
%V 8
%N 3
%U http://mmr.khu.ac.ir/article-1-3103-en.html
%R
%D 2022
%K The fractional q-derivativeو Difference formulaو Truncation errorوUnconditional Stabilityو The q-fractional differential equationو Convergence analysis.,
%X 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.
%> http://mmr.khu.ac.ir/article-1-3103-en.pdf
%P 116-91
%& 116
%!
%9 Original Manuscript
%L A-10-691-1
%+
%G eng
%@ 2588-2546
%[ 2022