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In this typescript, we study system of nonlinear implicit coupled differential equations of arbitrary (non–integer) order having nonlocal boundary conditions on closed interval [0, 1] with Caputo fractional derivative. We establish sufficient conditions for the existence, at least one and a unique solution of the proposed coupled system with the help of Krasnoselskii’s fixed point theorem and Banach contraction principle. Moreover, we scrutinize the Hyers–Ulam stability for the considered problem. We present examples to illustrate our main results.

This article is devoted to establish the existence of solution of ( α , β ) $\left(\alpha ,\beta \right)$ -order coupled implicit fractional differential equation with initial conditions, using Laplace transform method. The topological degree theory is used to obtain sufficient conditions for uniqueness and at least one solution of the considered system. Beside this, Ulam’s type stabilities are discussed for the proposed system. To support our main results, we present an example.

In this paper, the existence results of the solutions and stability are focused for impulsive implicit sequential fractional differential equation with multi-points boundary conditions. In view of the definitions of Caputo fractional order, the existence, uniqueness, and at least one solution of the aforesaid equation are presented. Beside this, Ulam’s type stabilities are discussed. To support our main results, we present some examples.

The main intention of the present research study is focused on the analysis of coupled impulsive fractional integrodifferential system having Hadamard derivatives. With the help of fixed point theorem attributed to Krasnoselskii’s, we investigate desired existence and uniqueness results. Moreover, we present different kinds of stability such as Hyers–Ulam stability, generalized Hyers–Ulam stability, Hyers–Ulam–Rassias stability, and generalized Hyers–Ulam–Rassias stability using the classical technique of functional analysis. Next, an example is designed to examine our findings based on the procedures applied in the theorems.

In this manuscript, switched coupled system of nonlinear impulsive Langevin equations involving four Hilfer fractional-order derivatives is considered. Using the techniques of nonlinear functional analysis, we establish appropriate conditions and results to discuss the existence, uniqueness, and Ulam’s type stability results of our proposed model, with the help of Schaefer’s fixed point theorem. An example is provided at the end to illustrate our results.

This work is committed to establishing the assumptions essential for at least one and unique solution of a switched coupled system of impulsive fractional differential equations having derivative of Hadamard type. Using Krasnoselskii’s fixed point theorem, the existence, as well as uniqueness results, is obtained. Along with this, different kinds of Hyers–Ulam stability are discussed. For supporting the theory, example is provided.

In this article, we make analysis of the implicit fractional differential equations involving integral boundary conditions associated with Stieltjes integral and its corresponding coupled system. We use some sufficient conditions to achieve the existence and uniqueness results for the given problems by applying the Banach contraction principle, Schaefer’s fixed point theorem, and Leray–Schauder result of the cone type. Moreover, we present different kinds of stability such as Hyers–Ulam stability, generalized Hyers–Ulam stability, Hyers–Ulam–Rassias stability, and generalized Hyers–Ulam–Rassias stability by using the classical technique of functional analysis. At the end, the results are verified with the help of examples.

In this manuscript, first we study the Hyers–Ulam stability of linear impulsive Volterra integral equations with the help of open mapping theorem approach. Then we give an existence and uniqueness theorem for the solutions of a class of nonlinear impulsive integral equations with a bounded variable delay. Moreover, with the help of integral inequality of Gronwall type, we investigate the Hyers–Ulam stability and Hyers–Ulam–Rassias stability of the same class of integral equations. We also present examples to support our main results.

We present some results on the existence, uniqueness and Hyers–Ulam stability to the solution of an implicit coupled system of impulsive fractional differential equations having Hadamard type fractional derivative. Using a fixed point theorem of Kransnoselskii’s type, the existence and uniqueness results are obtained. Along these lines, different kinds of Hyers–Ulam stability are discussed. An example is given to illustrate the main theorems.