AU - فتحی پور, اعظم
AU - fathipour, azam
TI - A distinct numerical approach for the solution of some kind of initial value problem involving nonlinear q-fractional differential equations
PT - JOURNAL ARTICLE
TA - khu-mmr
JN - khu-mmr
VO - 8
VI - 3
IP - 3
4099 - http://mmr.khu.ac.ir/article-1-3103-en.html
4100 - http://mmr.khu.ac.ir/article-1-3103-en.pdf
SO - khu-mmr 3
AB - 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.
CP - IRAN
IN - Me_samei@yahoo.com
LG - eng
PB - khu-mmr
PG - 116
PT - Original Manuscript
YR - 2022