Ulam‐Hyers‐Rassias stability for generalized fractional differential equations

Boucenna, Djalal; Makhlouf, Abdellatif Ben; El‐hady, El‐sayed; Hammami, Mohamed Ali

doi:10.1002/mma.7406

Cited by 7 publications

(7 citation statements)

References 37 publications

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“…First, suppose α ∈ [1, ∞). Using (11) and Lemmas 2.4 and 3.2, we have the inequality for t ≥ 0. Hence, we have…”

Section: Introduction Studies Have Investigated the Properties Of The...mentioning

confidence: 95%

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Approximate solutions of generalized logistic equation

Onitsuka

2024

DCDS-B

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This study investigates the behavior of the approximate solutions of the generalized logistic equation y ′ = y (1 − y α ), where α > 0. Based on the concept of Ulam stability, a concrete estimate of the amplitude of the difference between the approximate solution and the exact solution is obtained using the comparison principle and some sharp inequalities. The obtained results can be applied to the nonautonomous Richards model C ′ = r(t)C 1 − C α K .

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“…First, suppose α ∈ [1, ∞). Using (11) and Lemmas 2.4 and 3.2, we have the inequality for t ≥ 0. Hence, we have…”

Section: Introduction Studies Have Investigated the Properties Of The...mentioning

confidence: 95%

“…The papers [5,6,7,8,9,14,16,22,28,27,30,29,36,49] are the latest studies on Ulam stability for linear differential and difference equations. In addition, research on Ulam stability for fractional differential and difference equations has increased, e.g., [1,11,13,15,20,45,47].…”

Section: Introduction Studies Have Investigated the Properties Of The...mentioning

confidence: 99%

Approximate solutions of generalized logistic equation

Onitsuka

2024

DCDS-B

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“…Following this, the Ulam–Hyers stability theorem was used by a number of authors to study the stability issues and can be applied to the solution analysis of a wide variety of fractional differential equations [ 17 ]. In [ 18 ], a family of generalized nonlinear fractional differential equations of order alpha ( ) were subjected to the Ulam–Hyers stability theorem. For solutions to fractional differential equations in the unit disk, [ 19 ] looked at the Hyers–Ulam stability for fractional differential equations in a complex Banach space.…”

Section: Introductionmentioning

confidence: 99%

Analysis of mathematical model involving nonlinear systems of Caputo–Fabrizio fractional differential equation

Kebede

Lakoud

2023

Bound Value Probl

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In this paper, we consider a mathematical model of a coronavirus disease involving the Caputo–Fabrizio fractional derivative by dividing the total population into the susceptible population $\mathcal{S}(t)$ S ( t ) , the vaccinated population $\mathcal{V}(t)$ V ( t ) , the infected population $\mathcal{I}(t)$ I ( t ) , the recovered population $\mathcal{R}(t)$ R ( t ) , and the death class $\mathcal{D}(t)$ D ( t ) . A core goal of this study is the analysis of the solution of a proposed mathematical model involving nonlinear systems of Caputo–Fabrizio fractional differential equations. With the help of Lipschitz hypotheses, we have built sufficient conditions and inequalities to analyze the solutions to the model. Eventually, we analyze the solution for the formed mathematical model by employing Krasnoselskii’s fixed point theorem, Schauder’s fixed point theorem, the Banach contraction principle, and Ulam–Hyers stability theorem.

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“…Through the past six decades, the stability subject has been a common issue of investigations in many places (see, e.g., [12,15,22,23,9,20,21,25,27,26,28]). As a consequence of the interesting results presented in this direction, many articles devoted to this subject have been introduced ( [24,16,29] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

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

El‐hady

Makhlouf

Boulaaras

et al. 2022

Journal of Function Spaces

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Fractional derivatives are used to model the transmission of many real world problems like COVID-19. It is always hard to find analytical solutions for such models. Thus, approximate solutions are of interest in many interesting applications. Stability theory introduces such approximate solutions using some conditions. This article is devoted to the investigation of the stability of nonlinear differential equations with Riemann-Liouville fractional derivative. We employed a version of Banach fixed point theory to study the stability in the sense of Ulam-Hyers-Rassias (UHR). In the end, we provide a couple of examples to illustrate our results. In this way, we extend several earlier outcomes.

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Ulam‐Hyers‐Rassias stability for generalized fractional differential equations

Cited by 7 publications

References 37 publications

Approximate solutions of generalized logistic equation

Approximate solutions of generalized logistic equation

Analysis of mathematical model involving nonlinear systems of Caputo–Fabrizio fractional differential equation

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

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