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Novel Stability Results for Caputo Fractional Differential Equations

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  • Abdellatif Ben Makhlouf
  • El-Sayed El-Hady

Abstract

Modelling some diseases with large mortality rates worldwide, such as COVID-19 and cancer is crucial. Fractional differential equations are being extensively used in such modelling stages. However, exact analytical solutions for the solutions of such kind of equations are not reachable. Therefore, close exact solutions are of interests in many scientific investigations. The theory of stability in the sense of Ulam and Ulam–Hyers–Rassias provides such close exact solutions. So, this study presents stability results of some Caputo fractional differential equations in the sense of Ulam–Hyers, Ulam–Hyers–Rassias, and generalized Ulam–Hyers–Rassias. Two examples are introduced at the end to show the validity of our results. In this way, we generalize several recent interesting results.

Suggested Citation

  • Abdellatif Ben Makhlouf & El-Sayed El-Hady, 2021. "Novel Stability Results for Caputo Fractional Differential Equations," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-6, July.
    • Handle: RePEc:hin:jnlmpe:9817668
    DOI: 10.1155/2021/9817668
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    Cited by:

    1. Iskakova, Kulpash & Alam, Mohammad Mahtab & Ahmad, Shabir & Saifullah, Sayed & Akgül, Ali & Yılmaz, Gülnur, 2023. "Dynamical study of a novel 4D hyperchaotic system: An integer and fractional order analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 219-245.
    2. Kumar, Pushpendra & Erturk, Vedat Suat & Vellappandi, M. & Trinh, Hieu & Govindaraj, V., 2022. "A study on the maize streak virus epidemic model by using optimized linearization-based predictor-corrector method in Caputo sense," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).

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