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In this paper, we study the existence and uniqueness of solution for a problem consisting of a sequential nonlinear fractional Caputo-Langevin equation with nonlocal Riemann-Liouville fractional integral conditions. A variety of fixed point theorems, such as Banach's fixed point theorem, Krasnoselskii's fixed point theorem, Leray-Schauder's nonlinear alternative and Leray-Schauder degree theory, are used. Examples illustrating the obtained results are also presented.

In this paper, we study the existence and uniqueness of solutions for impulsive multi-orders Caputo-Hadamard fractional differential equations equipped with boundary and integral conditions. The Banach, Schaefer, and Rothe fixed point theorems and degree theory are used to establish our main results. Examples illustrating the main results are presented.

In this paper, we initiate the study of existence of solutions for a fractional differential system which contains mixed Riemann–Liouville and Hadamard–Caputo fractional derivatives, complemented with nonlocal coupled fractional integral boundary conditions. We derive necessary conditions for the existence and uniqueness of solutions of the considered system, by using standard fixed point theorems, such as Banach contraction mapping principle and Leray–Schauder alternative. Numerical examples illustrating the obtained results are also presented.

Impulsive multiorders fractional differential equations are studied. Existence and uniqueness results are obtained for first- and second-order impulsive initial value problems by using Banach’s fixed point theorem in an appropriate weighted space. Examples illustrating the main results are presented.