Volume 8, Issue 3 (Vol. 8,No. 3, 2022)                   mmr 2022, 8(3): 116-91 | Back to browse issues page

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1- , mesamei@gmail.com
Abstract:   (624 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.
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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

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