Note on the stability of first order linear differential equations

Bojor, Florin

doi:10.7494/opmath.2012.32.1.67

Cited by 8 publications

(2 citation statements)

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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%

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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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Section: Introductionmentioning

confidence: 99%

“…It should be remarked that Jung in [11] generalized the work of Alsina and Ger to the nonlinear case. In 2012, Bojor (see [12]) used different assumptions to study the stability of…”

Section: Introductionmentioning

confidence: 99%