Fractional Fourier Transform and Ulam Stability of Fractional Differential Equation with Fractional Caputo-Type Derivative

Selvam, A. George Maria; Sabarinathan, S.; Noeiaghdam, Samad; Govindan, Vediyappan

doi:10.1155/2022/3777566

Cited by 17 publications

(4 citation statements)

References 23 publications

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“…Later, Aoki [3] and Rassias [4] presented a generalized version of the stability results with the Cauchy difference as unbounded. Further, many researchers were attracted by the interesting stability result of various functional and differential equations [5–10].…”

Section: Introductionmentioning

confidence: 99%

Results on Ulam‐type stability of linear differential equation with integral transform

Selvam,

Sabarinathan,

Sooppy Nisar

et al. 2023

Math Methods in App Sciences

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The main theme of this study is to implement the Sumudu integral transform technique to solve the stability problem of linear differential equations. Another important aspect of this paper is to investigate the Ulam–Hyers and Ulam–Hyers–JRassias stability of linear differential equations by using Sumudu transform method. Further, the results are extended to the Mittag‐Leffler–Ulam–Hyers and Mittag‐Leffler–Ulam–Hyers–JRassias stability of these differential equations. As an application point of view, the Sumudu transform is used to find Ulam stabilities of differential equations arising in field‐controlled DC servo motor with position control.

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Section: Introductionmentioning

confidence: 99%

Results on Ulam‐type stability of linear differential equation with integral transform

Selvam,

Sabarinathan,

Sooppy Nisar

et al. 2023

Math Methods in App Sciences

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“…Khan and co-authors [9] investigated the Ulam-Hyers stability through fractal-fractional derivative with power law kernel and the chaotic system based on circuit design. As a result, a great number of papers (see, for instance, monographs [10,11], survey articles [12,13] and the references given there) on the subject have been published, generalizing Ulam's problem and Hyers's theorem in various directions and to other equations [14,15].…”

Section: Introductionmentioning

confidence: 99%

Ulam–Hyers Stability of Linear Differential Equation with General Transform

Pinelas,

Selvam,

Sabarinathan

2023

Symmetry

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The main aim of this study is to implement the general integral transform technique to determine Ulam-type stability and Ulam–Hyers–Mittag–Leffer stability. We are given suitable examples to validate and support the theoretical results. As an application, the general integral transform is used to find Ulam stability of differential equations arising in Thevenin equivalent electrical circuit system. The results are graphically represented, which provides a clear and thorough explanation of the suggested method.

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“…Moreover, it has been used to simulate physical, technical processes are best characterized by fractional differential equations (see Ahmad and Nieto (2009); Abdeljawad and Samei (2021); Brunt et al (2018); Hammad et al (2021) and references therein). Also, the stability of fractional order differential equation is an important and useful part of fractional differential equations and it has been introduced in several works Alzabut et al (2021); Hyers (1941); Jung (2006); Rus (2010); Rassias (2000); Hajiseyedazizi et al (2021); Ahmad et al (2020); Tang et al (2016); Shah and Tunc (2017); Kaabar et al (2021); Kalvandi et al (2019); Selvam et al (2022); Deepa et al (2022).…”

Section: Introductionmentioning

confidence: 99%

Stability analysis for a tripled system of fractional pantograph differential equations with nonlocal conditions

Hammad

Rashwan

Nafea

et al. 2023

Journal of Vibration and Control

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The goal of this article is to obtain the existence and uniqueness of a tripled fixed point to the underlying tripled system of fractional pantograph differential equations. We also used degree theory with non-local boundary conditions to derive relevant results supporting the existence of at least one solution to our proposed system. Furthermore, some stability analysis such as Ulam–Hyers and generalized Ulam–Hyers are established. Finally, an illustrative example is presented to support and enhance our analysis.

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Fractional Fourier Transform and Ulam Stability of Fractional Differential Equation with Fractional Caputo-Type Derivative

Abstract: In this paper, we study the Ulam-Hyers-Mittag-Leffler stability for a linear fractional order differential equation with a fractional Caputo-type derivative using the fractional Fourier transform. Finally, we provide an enumeration of the chemical reactions of the differential equation.

Cited by 17 publications

References 23 publications

Results on Ulam‐type stability of linear differential equation with integral transform

Results on Ulam‐type stability of linear differential equation with integral transform

Ulam–Hyers Stability of Linear Differential Equation with General Transform

Stability analysis for a tripled system of fractional pantograph differential equations with nonlocal conditions

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