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This paper is concerned with the existence of solutions for a fully coupled Riemann–Stieltjes, integro-multipoint, boundary value problem of Caputo-type sequential fractional differential equations. The given system is studied with the aid of the Leray–Schauder alternative and contraction mapping principle. A numerical example illustrating the abstract results is also presented.

We study a linear boundary value problem for systems of essentially loaded differential equations with an integro-multipoint condition. We make use of the numerical implementation of the Dzhumabaev parametrization method to obtain the desired result, which is well supported by two numerical examples.

Under different criteria, we prove the existence and uniqueness of solutions for a Riemann-Stieltjes integro-multipoint boundary value problem of Caputo-Riemann-Liouville type fractional integro-differential equations. Our results rely on the modern methods of functional analysis and are well-illustrated with the help of examples. Some interesting observations are also presented.

In this paper, the existence of a unique solution is established for a coupled system of Langevin fractional problems of ψ-Caputo fractional derivatives with generalized slit-strip-type integral boundary conditions and impulses using the Banach contraction principle. We also find at least one solution to the aforementioned system using some assumptions and Schaefer’s fixed point theorem. After that, Ulam–Hyers stability is discussed. Finally, to provide additional support for the main results, pertinent examples are presented.

We discuss the existence and uniqueness of solutions for a Caputo-type fractional order boundary value problem equipped with non-conjugate Riemann-Stieltjes integro-multipoint boundary conditions on an arbitrary domain. Modern tools of functional analysis are applied to obtain the main results. Examples are constructed for the illustration of the derived results. We also investigate different kinds of Ulam stability, such as Ulam-Hyers stability, generalized Ulam-Hyers stability, and Ulam-Hyers-Rassias stability for the problem at hand.

We investigate the existence of solutions for new boundary value problems of Caputo-type sequential fractional differential equations and inclusions supplemented with nonlocal integro-multipoint boundary conditions. We apply the modern techniques of functional analysis to obtain the main results. We emphasize that the results presented in this paper are new and specialize to some known theorems with an appropriate choice of the parameters involved in the problems at hand.