Ulam-Hyers-Rassias Stability of Nonlinear Differential Equations with Riemann-Liouville Fractional Derivative

El‐hady, El‐sayed; Makhlouf, Abdellatif Ben; Boulaaras, Salah; Mchiri, Lassaad

doi:10.1155/2022/7827579

Cited by 11 publications

(7 citation statements)

References 25 publications

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“…Hence, with the direct applications of the FDs, integral definitions and lemmas, it is clear that (10), ( 14) and ( 15) ⇒ (8). Hence the proof: FPT play a key role in many interesting recent outputs see, e.g., [20,21,35].…”

Section: Definition 4 ([34]mentioning

confidence: 80%

On Nonlinear Ψ-Caputo Fractional Integro Differential Equations Involving Non-Instantaneous Conditions

Arul¹,

Karthikeyan²,

Karthikeyan

et al. 2022

Symmetry

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We propose a solution to the symmetric nonlinear Ψ-Caputo fractional integro differential equations involving non-instantaneous impulsive boundary conditions. We investigate the existence and uniqueness of the solution for the proposed problem. Banach contraction theorem is employed to prove the uniqueness results, while Krasnoselkii’s fixed point technique is used to prove the existence results. Additionally, an example is used to explain the results. In this manner, our results represent generalized versions of some recent interesting contributions.

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Section: Definition 4 ([34]mentioning

confidence: 80%

On Nonlinear Ψ-Caputo Fractional Integro Differential Equations Involving Non-Instantaneous Conditions

Arul¹,

Karthikeyan²,

Karthikeyan

et al. 2022

Symmetry

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“…Fixed-point theorems have recently played a vital role in proving many interesting results (see, e.g., [39][40][41]).…”

Section: Existence Resultsmentioning

confidence: 99%

On Coupled System of Langevin Fractional Problems with Different Orders of μ-Caputo Fractional Derivatives

et al. 2023

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In this paper, we study coupled nonlinear Langevin fractional problems with different orders of μ-Caputo fractional derivatives on arbitrary domains with nonlocal integral boundary conditions. In order to ensure the existence and uniqueness of the solutions to the problem at hand, the tools of the fixed-point theory are applied. An overview of the main results of this study is presented through examples.

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“…Lemma 1. The region of the system (8) with the initial conditions (9) given by Ì + U 6  , is positively invariant in + .…”

Section: Invariant Regionmentioning

confidence: 99%

“…In fractional calculus, the derivative and integral operators are generalized to fractional orders, such as 1/2 or 3/4. These operators can be defined using fractional calculus techniques, such as the Caputo operators [5][6][7][8] and Riemann-Liouville [9,10]. One of the key features of fractional calculus is that it allows for the study of phenomena that exhibit long-term memory, such as anomalous diffusion, fractional Brownian motion, and viscoelasticity.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of fractional epidemic model for two infected classes incorporating hospitalization impact

Santra,

Mahapatra,

Basu

2024

Phys. Scr.

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This article presents an epidemic disease propagation mathematical model in fractional order. The epidemiological characteristics are presented based on the susceptible, exposed, unknown infected, known infected, hospitalized population and the population in the secure zone. Both the disease endemic equilibrium and the disease-free equilibrium's stability characteristics have been examined using the basic reproduction number. Variation of basic reproduction number based on the different sensitive parameters has been discussed. It has been disputed whether the fractional model provides a uniform, reliable solution. An analysis of the time history of unknown and known infected populations, hospitalized populations and recovered populations at different values of various sensitive parameters has been carried out. To support the key theoretical conclusions, some numerical simulations are completed using MATLAB. The impact of various populations on the propagation of the illness has also been investigated, as well as how specific state variables change over time for various fractional order values.

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Ulam-Hyers-Rassias Stability of Nonlinear Differential Equations with Riemann-Liouville Fractional Derivative

Cited by 11 publications

References 25 publications

On Nonlinear Ψ-Caputo Fractional Integro Differential Equations Involving Non-Instantaneous Conditions

On Nonlinear Ψ-Caputo Fractional Integro Differential Equations Involving Non-Instantaneous Conditions

On Coupled System of Langevin Fractional Problems with Different Orders of μ-Caputo Fractional Derivatives

Stability analysis of fractional epidemic model for two infected classes incorporating hospitalization impact

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