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A distinct numerical approach for the solution of some kind of initial value problem involving nonlinear q-fractional differential equations
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| اعظم فتحی پور1, Azam Fathipour |
| 1- , mesamei@gmail.com |
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Abstract: (121 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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| Keywords: The fractional q-derivativeو Difference formulaو Truncation errorوUnconditional Stabilityو The q-fractional differential equationو Convergence analysis. |
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Full-Text [PDF 1777 kb]
(31 Downloads)
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Type of Study: Original Manuscript |
Subject:
Mat
Received: 2019/12/18 | Revised: 2022/12/20 | Accepted: 2020/12/22 | Published: 2022/12/20 | ePublished: 2022/12/20
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