On Nonlinear Fractional Difference Equation with Delay and Impulses

Ouncharoen, Rujira; Chasreechai, Saowaluck; Sitthiwirattham, Thanin

doi:10.3390/sym12060980

Cited by 2 publications

(1 citation statement)

References 42 publications

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“…In the past ten years, there has been a significant increase in the quantity of research in discrete fractional calculus. For an extensive collection of more knowledge in this field, we refer the readers to [15][16][17][18][19][20][21][22][23][24][25][26][27] and the references therein. In [16], Goodrich investigated a discrete fractional boundary value problem (FBVP) of the form…”

Section: Introductionmentioning

confidence: 99%

Existence and Hyers–Ulam Stability of Solutions for a Mixed Fractional-Order Nonlinear Delay Difference Equation with Parameters

Luo

Qiu

2020

Mathematical Problems in Engineering

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This paper focuses on a kind of mixed fractional-order nonlinear delay difference equations with parameters. Under some new criteria and by applying the Brouwer theorem and the contraction mapping principle, the new existence and uniqueness results of the solutions have been established. In addition, we deduce that the solution of the addressed equation is Hyers–Ulam stable. Some results in the literature can be generalized and improved. As an application, three typical examples are delineated to demonstrate the effectiveness of our theoretical results.

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Section: Introductionmentioning

confidence: 99%

Existence and Hyers–Ulam Stability of Solutions for a Mixed Fractional-Order Nonlinear Delay Difference Equation with Parameters

Luo

Qiu

2020

Mathematical Problems in Engineering

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Existence results of sequential fractional Caputo sum-difference boundary value problem

Metpattarahiran¹,

Linitda²,

Sitthiwirattham

2022

MATH

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<abstract><p>In this article, we study the existence and uniqueness results for a sequential nonlinear Caputo fractional sum-difference equation with fractional difference boundary conditions by using the Banach contraction principle and Schaefer's fixed point theorem. Furthermore, we also show the existence of a positive solution. Our problem contains different orders and four fractional difference operators. Finally, we present an example to display the importance of these results.</p></abstract>

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On Nonlinear Fractional Difference Equation with Delay and Impulses

Cited by 2 publications

References 42 publications

Existence and Hyers–Ulam Stability of Solutions for a Mixed Fractional-Order Nonlinear Delay Difference Equation with Parameters

Existence and Hyers–Ulam Stability of Solutions for a Mixed Fractional-Order Nonlinear Delay Difference Equation with Parameters

Existence results of sequential fractional Caputo sum-difference boundary value problem

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