Volume 8, Issue 3 (Vol. 8,No. 3, 2022)
mmr 2022, 8(3): 116-91 |
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فتحی پور ا, fathipour A. A distinct numerical approach for the solution of some kind of initial value problem involving nonlinear q-fractional differential equations. mmr 2022; 8 (3) :116-91
URL: http://mmr.khu.ac.ir/article-1-3103-en.html
URL: http://mmr.khu.ac.ir/article-1-3103-en.html
1- , mesamei@gmail.com
Abstract: (1193 Views)
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.
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.
Type of Study: Original Manuscript |
Subject:
Mat
Received: 2019/12/18 | Revised: 2023/06/18 | Accepted: 2020/12/22 | Published: 2022/12/20 | ePublished: 2022/12/20
Received: 2019/12/18 | Revised: 2023/06/18 | Accepted: 2020/12/22 | Published: 2022/12/20 | ePublished: 2022/12/20
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