Fractional Differential Inclusions Research Articles

Solvability for a system of Hadamard-type hybrid fractional differential inclusions

Abstract In this article, a new system of Hadamard-type hybrid fractional differential inclusions equipped with Dirichlet boundary conditions was constructed. By virtue of a fixed-point theorem due to B. C. Dhage, (Existence results for neutral functional differential inclusions in Banach algebras, Nonlinear Anal. 64 (2006), no. 6, 1290–1306, doi: https://doi.org/10.1016/j.na.2005.06.036), the existence results of solutions for the considered problem are derived in a new norm space for multivalued maps. A numerical example is provided to illustrate our main results.

Oscillation and nonoscillation for Caputo-Hadamard fractional differential inclusions in Banach spaces

Oscillation and nonoscillation for Caputo-Hadamard fractional differential inclusions in Banach spaces

Approximate Controllability of Fractional Stochastic Evolution Inclusions with Non-Local Conditions

This article investigates the approximate controllability of non-linear fractional stochastic differential inclusions with non-local conditions. We establish a set of sufficient conditions for their approximate controllability and provide results in terms of controllability for the fractional stochastic control system. Our approach relies on using fractional calculus and the fixed-point theorem for multiple-valued operators. Finally, we present an illustrative example to support our findings.

The Existence Theorems of Fractional Differential Equation and Fractional Differential Inclusion with Affine Periodic Boundary Value Conditions

This paper is devoted to investigating the existence of solutions for the fractional differential equation and fractional differential inclusion of order α∈(2,3] with affine periodic boundary value conditions. Applying the Leray–Schauder fixed point theorem, the existence of the solutions for the fractional differential equation is established. Furthermore, for the fractional differential inclusion, we consider two cases: (i) the set-valued function has convex value and (ii) the set-valued function has nonconvex value. The main tools of our research are the Leray–Schauder alternative theorem, Covita and Nadler’s fixed point theorem and some set-valued analysis theories.

Existence Results for Caputo Tripled Fractional Differential Inclusions with Integral and Multi-Point Boundary Conditions

In this study, based on Coitz and Nadler’s fixed point theorem and the non-linear alternative for Kakutani maps, existence results for a tripled system of sequential fractional differential inclusions (SFDIs) with integral and multi-point boundary conditions (BCs) in investigated. A practical examples are given to illustrate the obtained the theoretical results.

Multipoint boundary value problems for higher-order Hadamard fractional neutral differential equations and inclusions

In this paper, we consider fractional neutral differential equations with multipoint boundary value conditions involving Hadamard derivatives and integrals. We obtain the existence and uniqueness of the solution of the equation by using several fixed point theorems, and we also consider the Ulam–Hyers stability of the solution. In addition, we study the differential inclusion problem with multipoint boundary value conditions and prove the existence of the solution of the boundary value problem when the multivalued map has convex values. We also give several examples to illustrate the feasibility of the results.

The exponential nature and solvability of stochastic multi-term fractional differential inclusions with Clarke’s subdifferential

This study explores a new class of stochastic multi-term fractional differential inclusions with the Clarke subdifferential involving the Rosenblatt process. The presence and uniqueness of a solution are determined by the successive approximation approach in combination with the stochastic analysis methodology and the resolvent operators. Furthermore, new sufficient conditions are given to ensure the exponential decay of the mild solution without Lipschitz conditions on non-linear terms. We have also provided an example to validate the obtained results.

Boundary value problems for sequential Hilfer fractional differential equations and inclusions with integro-multistrip-multipoint boundary conditions

Boundary value problems for sequential Hilfer fractional differential equations and inclusions with integro-multistrip-multipoint boundary conditions

On Cauchy Problems of Caputo Fractional Differential Inclusion with an Application to Fractional Non-Smooth Systems

In this innovative study, we investigate the properties of existence and uniqueness of solutions to initial value problem of Caputo fractional differential inclusion. In the study of existence problems, we considered the case of convex and non-convex multivalued maps. We obtained the existence results for both cases by means of the appropriate fixed point theorem. Furthermore, the uniqueness corresponding to both cases was also determined. Finally, we took a non-smooth system, the modified Murali–Lakshmanan–Chua (MLC) fractional-order circuit system, as an example to verify its existence and uniqueness conditions, and through several sets of simulation results, we discuss the implications.

Decay mild solutions of Hilfer fractional differential variational–hemivariational inequalities

The primary objective of this paper is to explore a decay mild solution governed by a class of dynamical systems, called Hilfer fractional differential variational–hemivariational inequality (HFDVHVI, for short), which is composed of a Hilfer fractional evolution differential inclusion and a variational–hemivariational inequality involving two history-dependent operators in the framework of spaces. Our first aim is to investigate the solvability of the mild solutions to (HFDVHVI) by means of fixed point principle. The second step of the paper is to study the existence of decay mild solutions to (HFDVHVI) via giving expression for the Mittag-Leffler function and the Wright function.

Exploration nonlocal controllability for Hilfer fractional differential inclusions with Clarke subdifferential and nonlinear noise

In this study, we deal with the control system described by nonlocal Hilfer fractional differential inclusions with Clarke subdifferential and nonlinear noise. By using fractional calculus, stochastic analysis, properties of Clarke subdifferential and non-smooth analysis, nonlocal controllability for the considered problem are established. Finally, an example is given to illustrate the obtained results.

Approximate controllability of Sobolev-type Atangana-Baleanu fractional differential inclusions with noise effect and Poisson jumps

<abstract><p>In this paper, we explore the approximative controllability of fractional stochastic differential inclusions (SDIs) of Sobolev-type with fractional derivatives in Atangana-Baleanu (AB) sense and Poisson jumps. Our findings are supported by the fixed point theorem, multi-valued map theory, compact semigroup theory and stochastic analysis principles. In the later part, an illustration is provided to clarify the established outcomes.</p></abstract>

Controllability of Hilfer type fractional evolution neutral integro-differential inclusions with non-instantaneous impulses

<p style='text-indent:20px;'>In this manuscript the controllability of Hilfer fractional neutral differential inclusions with non-instantaneous impulse in Banach space is investigated by using semi-group theory, fractional calculus, upper semi-continuous (u.s.c), multi-functions and Mönch fixed point theorem. Sufficient conditions are derived by using Hausdorff measure of non-compactness (MNC). Further, the obtained result is illustrated by an example.</p>

Nonlocal semilinear Ф-Caputo fractional evolution equation with a measure of noncompactness in Banach space

The aim of this work is to study the existence of solutions for nonlocal fractional differential equations inclusions involving ?-Caputo fractional dirivative in Banach space. The proofs are based on the noncompactness measure method. As application, we give an example is given to illustrate the theoretical results.

Existence of solution for some φ-Caputo fractional differential inclusions Viawardowski-Mizoguchi-Takahashi multi-valued contractions

In this study, we examine the existence of solution for some ?-Caputo fractional differential inclusions with arbitrary coefficients with boundary values using Wardowski-Mizoguchi-Takahashi multivalued contractions. Our results utilize some existence results regarding ?-Caputo fractional differential inclusions, in particular the results of Belmor et al. (2021). Our key findings are illustrated with an example.

Relaxation in nonconvex optimal control problems described by evolution Riemann-Liouville fractional differential inclusions

<p style='text-indent:20px;'>In this paper, we are concerned with the minimization problem of an integral functional with integrand that is not convex in the control on solutions of a Riemann-Liouville fractional differential control system with mixed nonconvex feedback constraints on the control. At First, the existence results for Riemann-Liouville fractional semilinear differential control systems are discussed by using Schauder's fixed point theorem. Under some reasonable assumptions, we prove that the relaxation problem has an optimal solution, and that for each optimal solution there has a minimizing sequence of the original problem that converges to the optimal solution with respect to the trajectory, the control, and the functional in appropriate topologies simultaneously. Finally, we give an example to illustrate our main results.</p>

On topological properties of solution sets of semilinear fractional differential inclusions with non-convex right-hand side

On topological properties of solution sets of semilinear fractional differential inclusions with non-convex right-hand side

SEVERAL VARIATIONAL INCLUSIONS FOR A FRACTIONAL DIFFERENTIAL INCLUSION OF CAPUTO-FABRIZIO TYPE

We establish several fractional variational inclusions for solutions of a nonconvex fractional differential inclusion involving Caputo-Fabrizio fractional derivative.

On Fractional Differential Inclusion for an Epidemic Model via L-Fuzzy Fixed Point Results

On Fractional Differential Inclusion for an Epidemic Model via L-Fuzzy Fixed Point Results

Existence of solutions to Caputo fractional differential inclusions of $ 1 < \alpha < 2 $ with initial and impulsive boundary conditions

<abstract><p>This paper is concerned with the existence of solutions to the Caputo fractional differential inclusion of $ 1 < \alpha < 2 $ with initial and impulsive boundary conditions. A novel existence result is presented based on the fixed-point theorem of Dhage for multi-valued operators with some assumptions. Finally, two examples are provided to explicate the applicability of the main result.</p></abstract>