We study the existence of mild solutions for a class of impulsive fractional partial neutral integro-differential inclusions with state-dependent delay. We assume that the undelayed part generates an α-resolvent operator and transform it into an integral equation. Sufficient conditions for the existence of solutions are derived by means of the fixed point theorem for discontinuous multi-valued operators due to Dhage and properties of the α-resolvent operator. An example is given to illustrate the...

This paper is devoted to studying the existence of solutions of a nonlocal initial value problem involving generalized Katugampola fractional derivative. By using fixed point theorems, the results are obtained in weighted space of continuous functions. Illustrative examples are also given.

A class of impulsive boundary value problems of fractional differential systems is studied. Banach spaces are constructed and nonlinear operators defined on these Banach spaces. Sufficient conditions are given for the existence of solutions of this class of impulsive boundary value problems for singular fractional differential systems in which odd homeomorphism operators (Definition 2.6) are involved. Main results are Theorem 4.1 and Corollary 4.2. The analysis relies on a well known fixed point...

In this paper, we consider the following boundary value problem $$\left\{\begin{array}{c}{D}_{T^{-}}^{\alpha }\left(D_{0^{+}}^{\alpha }\left(D_{T^{-}}^{\alpha }\left(D_{0^{+}}^{\alpha }u\left(t\right)\right)\right)\right)=f(t,u\left(t\right)),t\in [0,T],\hfill \\ u\left(0\right)=u\left(T\right)=0\hfill \\ D_{T^{-}}^{\alpha }\left(D_{0^{+}}^{\alpha }u\left(0\right)\right)=D_{T^{-}}^{\alpha }\left(D_{0^{+}}^{\alpha }u\left(T\right)\right)=0,\hfill \end{array}\right.$$ where $0<\alpha \le 1$ and $f:[0,T]\times ℝ\to ℝ$ is a continuous function, $D_{0^{+}}^{\alpha }$, $D_{T^{-}}^{\alpha }$ are respectively the left and right fractional Riemann–Liouville derivatives and we prove the existence of at least one solution for this problem.

Mathematics Subject Classification: 26A33, 34A60, 34K40, 93B05In this paper we investigate the existence of solutions for fractional functional differential inclusions with infinite delay. In the last section we present an application of our main results in control theory.

This paper presents several sufficient conditions for the existence of at least one classical solution to impulsive fractional differential equations with a $p$-Laplacian and Dirichlet boundary conditions. Our technical approach is based on variational methods. Some recent results are extended and improved. Moreover, a concrete example of an application is presented.

In this article, we study the existence of solutions to systems of conformable fractional differential equations with periodic boundary value or initial value conditions. where the right member of the system is $L_{\alpha }^1$-carathéodory function. We employ the method of solution-tube and Schauder’s fixed-point theorem.

In this paper we consider the existence, multiplicity, and nonexistence of positive solutions to fractional differential equation with integral boundary conditions. Our analysis relies on the fixed point index.

In this work, we communicate the topic of complex Lie algebroids based on the extended fractional calculus of variations in the complex plane. The complexified Euler-Lagrange geodesics and Wong's fractional equations are derived. Many interesting consequences are explored.