A DIFFERENCE METHOD FOR SOLVING THE NONLINEAR q-FRACTIONAL DIFFERENTIAL EQUATIONS ON TIME SCALES

The [Formula: see text]-fractional differential equation usually describes the physics process imposed on the time scale set [Formula: see text]. In this paper, we first propose a difference formula for discretizing the fractional [Formula: see text]-derivative [Formula: see text] on the time scale set [Formula: see text] with order [Formula: see text] and scale index [Formula: see text]. We establish a rigours truncation error boundness and prove that this difference formula is unconditionally stable. Then, we consider the difference method for solving the initial value problem of [Formula: see text]-fractional differential equation: [Formula: see text] on the time scale set. 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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Existence and stability of a nonlinear fractional differential equation involving a $\psi$-Caputo operator

Advances in the Theory of Nonlinear Analysis and its Application ◽

10.31197/atnaa.664534 ◽

2020 ◽

Author(s):

Hanan A. WAHASH ◽

Mohammed ABDO ◽

Satish PANCHAL

Keyword(s):

Differential Equation ◽

Fractional Differential Equation ◽

Nonlinear Fractional Differential Equation ◽

Existence And Stability ◽

Fractional Differential

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On the existence and stability of fuzzy CF variable fractional differential equation for COVID-19 epidemic

Engineering With Computers ◽

10.1007/s00366-021-01296-9 ◽

2021 ◽

Author(s):

Pratibha Verma ◽

Manoj Kumar

Keyword(s):

Differential Equation ◽

Fractional Differential Equation ◽

Existence And Stability ◽

Fractional Differential

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Existence and stability of solution for a nonlinear fractional differential equation

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2020.124921 ◽

2021 ◽

pp. 124921

Author(s):

Jue-liang Zhou ◽

Shu-qin Zhang ◽

Yu-bo He

Keyword(s):

Differential Equation ◽

Fractional Differential Equation ◽

Nonlinear Fractional Differential Equation ◽

Stability Of Solution ◽

Existence And Stability ◽

Fractional Differential

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Existence and stability of some nonlinear ψ-Hilfer partial fractional differential equation

Partial Differential Equations in Applied Mathematics ◽

10.1016/j.padiff.2021.100032 ◽

2021 ◽

pp. 100032

Author(s):

Deepak B. Pachpatte

Keyword(s):

Differential Equation ◽

Fractional Differential Equation ◽

Existence And Stability ◽

Fractional Differential ◽

Partial Fractional Differential Equation

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Unique existence of solution to initial value problem for fractional differential equation involving with fractional derivative of variable order

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2021.111040 ◽

2021 ◽

Vol 148 ◽

pp. 111040

Author(s):

Shuqin Zhang ◽

Xinwei Su

Keyword(s):

Differential Equation ◽

Fractional Derivative ◽

Fractional Differential Equation ◽

Initial Value Problem ◽

Existence Of Solution ◽

Variable Order ◽

Initial Value ◽

Unique Existence ◽

Fractional Differential

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Inverse source problem for the abstract fractional differential equation

Journal of Inverse and Ill-Posed Problems ◽

10.1515/jiip-2020-0038 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Andrey B. Kostin ◽

Sergey I. Piskarev

Keyword(s):

Differential Equation ◽

Fractional Differential Equation ◽

Operator Function ◽

Compact Semigroup ◽

Inverse Source Problem ◽

Final Point ◽

Existence And Stability ◽

Fractional Differential ◽

The Right ◽

Stability Of The Solution

AbstractIn a Banach space, the inverse source problem for a fractional differential equation with Caputo–Dzhrbashyan derivative is considered. The initial and observation conditions are given by elements from D(A), and the operator function on the right side is sufficiently smooth. Two types of the observation operator are considered: integral and at the final point. Under the assumptions that operator 𝐴 is a generator of positive and compact semigroup the uniqueness, existence and stability of the solution are proved.

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