Finite time stability (FTS) of fractional-order time delayed systems (FOTDSs) has been studied by many researchers based on the Lyapunov functions and Gronwall inequalities. In this paper, we proposed a novel FTS scheme for FOTDSs based on the fixed point theory. By exploiting the fixed point approach, sufficient conditions that guarantee the robust FTS of FOTDSs have been established. Finally, two illustrative examples are presented to validate the main result.

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.

In this paper, stability analysis which ensures the convergence of a part of the solutions towards a ball of a class of fractional‐order nonlinear systems is described. Using the Lyapunov‐like functions, such nonlinear systems depending on a small parameter is studied, and such practical stability is ensured. Numerical examples are given to illustrate the validity of the proposed theoretical results as well as a real application to a class of cobweb models.

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.

Differential equations with fractional derivative are being extensively used in the modelling of the transmission of many infective diseases like HIV, Ebola, and COVID-19. Analytical solutions are unreachable for a wide range of such kind of equations. Stability theory in the sense of Ulam is essential as it provides approximate analytical solutions. In this article, we utilize some fixed point theorem (FPT) to investigate the stability of fractional neutral integrodifferential equations with delay in the sense of Ulam-Hyers-Rassias (UHR). This work is a generalized version of recent interesting works. Finally, two examples are given to prove the applicability of our results.