Existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems

summary:We study the existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems. Our results are based on Schauder's fixed point theorem and the Banach contraction principle fixed point theorem. Examples are provided to illustrate the main results

On existence results for hybrid ψ−\psi-Caputo multi-fractional differential equations with hybrid conditions

In this paper, we study the existence and uniqueness results of a fractional hybrid boundary value problem with multiple fractional derivatives of $\psi-$Caputo with different orders. Using a useful generalization of Krasnoselskii’s fixed point theorem, we have established results of at least one solution, while the uniqueness of solution is derived by Banach's fixed point. The last section is devoted to an example that illustrates the applicability of our results

Fractional hybrid differential equations with three-point boundary hybrid conditions

Abstract In this paper, we study the existence of solutions for hybrid fractional differential equations involving fractional Caputo derivative of order 1<α≤2 $1 < \alpha\leq 2$. Our results rely on a hybrid fixed point theorem for a sum of three operators due to Dhage. An example is provided to illustrate the theory

Existence results for impulsive semilinear fractional differential inclusions with delay in Banach spaces

In this paper, we introduce a new concept of mild solution of some class of semilinear fractional differential inclusions of order 0 < α < 1. Also we establish an existence result when the multivalued function has convex values. The result is obtained upon the nonlinear alternative of Leray-Schauder type

Controllability of impulsive semilinear functional differential inclusions with finite delay in Fréchet spaces

In this paper, we use the extrapolation method combined with a recent nonlinear alternative of Leray-Schauder type for multivalued admissible contractions in Fréchet spaces to study the existence of a mild solution for a class of first order semilinear impulsive functional differential inclusions with finite delay, and with operator of nondense domain in original space

Impulsive semilinear neutral functional differential inclusions with multivalued jumps

summary:In this paper we establish sufficient conditions for the existence of mild solutions and extremal mild solutions for some densely defined impulsive semilinear neutral functional differential inclusions in separable Banach spaces. We rely on a fixed point theorem for the sum of completely continuous and contraction operators

Novel Method for Generalized Stability Analysis of Nonlinear Impulsive Evolution Equations

summary:In this paper, we discuss some generalized stability of solutions to a class of nonlinear impulsive evolution equations in the certain piecewise essentially bounded functions space. Firstly, stabilization of solutions to nonlinear impulsive evolution equations are studied by means of fixed point methods at an appropriate decay rate. Secondly, stable manifolds for the associated singular perturbation problems with impulses are compared with each other. Finally, an example on initial boundary value problem for impulsive parabolic equations is illustrated to our theory results