In this paper, existence and uniqueness of solution for a coupled impulsive Hilfer–Hadamard type fractional differential system are obtained by using Kransnoselskii’s fixed point theorem. Different types of Hyers–Ulam stability are also discussed.We provide an example demonstrating consistency to the theoretical findings.

This paper deals with existence, uniqueness, and Hyers-Ulam stability of solutions to a nonlinear coupled implicit switched singular fractional differential system involving Laplace operator φ p. The proposed problem consists of two kinds of fractional derivatives, that is, Riemann-Liouville fractional derivative of order β and Caputo fractional derivative of order σ , where m-1 < β, σ < m, m ∈ {2, 3,. .. }. Prior to proceeding to the main results, the system is converted into an equivalent integral form by the help of Green's function. Using Schauder's fixed point theorem and Banach's contraction principle, the existence and uniqueness of solutions are proved. The main results are demonstrated by an example.

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.

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In this article, we study the existence and uniqueness of solutions of a switched coupled implicit ψ-Hilfer fractional differential system. The existence and uniqueness results are obtained by using fixed point techniques. Further, we investigate different kinds of stability such as Hyers–Ulam stability and Hyers–Ulam–Rassias stability. Finally, an example is provided to illustrate the obtained results.