Solutions For Fractional Differential Inclusions Research Articles

Existence of solutions for fractional differential inclusions with initial value condition and non-instantaneous impulses

In this paper, we mainly consider the existence of solutions for a kind of ?-Hilfer fractional differential inclusions involving non-instantaneous impulses. Utilizing another nonlinear alternative of Leray-Schauder type, we present a new constructive result for the addressed system with the help of generalized Gronwall inequality and Lagrange mean-value theorem, and some achievements in the literature can be generalized and improved. As an application, a typical example is delineated to demonstrate the effectiveness of our theoretical results.

Mild solutions to fractional differential inclusions with nonlocal conditions

This article is concerned with the existence of mild solutions for fractional differential inclusions with nonlocal conditions in Banach spaces. The results are obtained by using fractional calculus, Hausdorff measure of noncompactness, and the multivalued fixed point theorem. The results obtained in the present paper extend some related results on this topic.

On General Fractional Differential Inclusions with Nonlocal Integral Boundary Conditions

This paper investigates the existence of solutions for fractional differential inclusions involving Caputo fractional derivative of any order together with nonlocal integral boundary conditions. Our study includes the cases when the multivalued map involved in the problem has convex as well as non-convex values. Some standard fixed point theorems for multivalued maps are applied to establish the main results, which are well illustrated with the aid of examples.

On the existence of positive solutions for fractional differential inclusions at resonance.

In this paper, we discuss the existence of positive solutions for a boundary value problem of fractional differential inclusions with resonant boundary conditions. By using the Leggett–Williams theorem for coincidences of multi-valued operators due to O’Regan and Zima, results on the existence of positive solutions are established. An example is given to illustrate the efficiency of the main theorems.

Existence of solutions for fractional differential inclusions with integral boundary conditions

In this paper, we study the existence of solutions for a new class of boundary value problems for nonlinear fractional differential inclusions with mixed type integral boundary conditions. The cases when the multifunction has convex as well as non-convex values are considered. Our results rely on the standard tools of fixed point theory and are well illustrated with the aid of an example.

On the existence of solutions for fractional differential inclusions with sum and integral boundary conditions

In this paper, by using the endpoint result for multifunctions, we investigate the existence of solutions for a boundary value problem for fractional differential inclusions with sum and integral boundary conditions. Finally, an example is also given to illustrate the validity of our main result.

Existence of solutions for fractional differential inclusions with nonlocal Riemann-Liouville integral boundary conditions

In this paper, we discuss the existence of solutions for a boundary value problem of fractional differential inclusions with nonlocal Riemann-Liouville integral boundary conditions. Our results include the cases when the multivalued map involved in the problem is (i) convex valued, (ii) lower semicontinuous with nonempty closed and decomposable values and (iii) nonconvex valued. In case (i) we apply a nonlinear alternative of Leray-Schauder type, in the second case we combine the nonlinear alternative of Leray-Schauder type for single-valued maps with a selection theorem due to Bressan and Colombo, while in the third case we use a fixed point theorem for multivalued contractions due to Covitz and Nadler.

On fractional differential inclusions with anti-periodic type integral boundary conditions

Abstract This paper investigates the existence of solutions for fractional differential inclusions of order q ∈ ( 2 , 3 ] with anti-periodic type integral boundary conditions by means of some standard fixed point theorems for inclusions. Our results include the cases when the multivalued map involved in the problem has convex as well as non-convex values. The paper concludes with an illustrative example. MSC:34A60, 34A08.

Existence of solutions for fractional differential inclusions with four-point nonlocal Riemann-Liouville type integral boundary conditions

This paper presents some existence results for a new class of nonlocal boundary value problems of fractional differential inclusions with four-point nonlocal Riemann-Liouville type integral boundary conditions. Our results are based on some fixed point principles for multivalued maps.

Existence of Solutions for Fractional Differential Inclusions with Separated Boundary Conditions in Banach Space

We discuss the existence of solutions for a class of some separated boundary differential inclusions of fractional orders2<α<3involving the Caputo derivative. In order to obtain necessary conditions for the existence result, we apply the fixed point technique, fractional calculus, and multivalued analysis.

A note on the existence of solutions for some boundary value problems of fractional differential inclusions

Abstract We study the existence of solutions for fractional differential inclusions of order q ∈ (1, 2] with families of mixed and closed boundary conditions. We establish Filippov type existence results in the case of nonconvex setvalued maps.

Existence of solutions for fractional differential inclusions with nonlocal strip conditions

In this paper, we discus the existence of solutions for a nonlocal boundary value problem of fractional differential inclusions concerning a nonlocal strip condition via some fixed point theorems. Our results include the cases when the right-hand side of the inclusion is convex as well as nonconvex valued.

On the existence of solutions for fractional differential inclusions with anti-periodic boundary conditions

The existence of solutions of an anti-periodic boundary value problem for fractional differential inclusions of order α∈(2,3] is investigated. Several results are obtained by using suitable fixed point theorems when the right hand side has convex or non convex values.

Existence of Solutions for Fractional Differential Inclusions with Antiperiodic Boundary Conditions

We study the existence of solutions for a class of fractional differential inclusions with anti-periodic boundary conditions. The main result of the paper is based on Bohnenblust- Karlins fixed point theorem. Some applications of the main result are also discussed.