Existence Results for ψ -Hilfer Fractional Integro-Differential Hybrid Boundary Value Problems for Differential Equations and Inclusions

In this research work, we study a new class of ψ -Hilfer hybrid fractional integro-differential boundary value problems with nonlocal boundary conditions. Existence results are established for single and multivalued cases, by using suitable fixed-point theorems for the product of two single or multivalued operators. Examples illustrating the main results are also constructed.

A Survey on Existence Results for Boundary Value Problems of Hilfer Fractional Differential Equations and Inclusions

This paper is a survey of the recent results of the author for various classes of boundary value problems for Hilfer fractional differential equations and inclusions of fractional order in (1,2] supplemented with different kinds of nonlocal boundary conditions.

Existence criteria via α–ψ-contractive mappings of φ-fractional differential nonlocal boundary value problems

In the existing study, we investigate the criteria of existence of solution for relatively new categories of φ-Caputo fractional differential equations and inclusions problems equipped with nonlocal φ-integral boundary conditions. In order to achieve the desired goal, we use α–ψ-contractive mappings and the theory of approximate endpoint. In the final stage, we exhibit some examples to provide the illustrations of our theoretical findings.

Boundary value problems for Hilfer type sequential fractional differential equations and inclusions involving Riemann–Stieltjes integral multi-strip boundary conditions

In this paper, we study boundary value problems for sequential fractional differential equations and inclusions involving Hilfer fractional derivatives, supplemented with Riemann–Stieltjes integral multi-strip boundary conditions. Existence and uniqueness results are obtained in the single-valued case by using the classical Banach and Krasnosel’skiĭ fixed point theorems and the Leray–Schauder nonlinear alternative. In the multi-valued case an existence result is proved by using nonlinear alternative for contractive maps. Examples illustrating our results are also presented.

Boundary Value Problems for ψ-Hilfer Type Sequential Fractional Differential Equations and Inclusions with Integral Multi-Point Boundary Conditions

In the present article, we study a new class of sequential boundary value problems of fractional order differential equations and inclusions involving ψ-Hilfer fractional derivatives, supplemented with integral multi-point boundary conditions. The main results are obtained by employing tools from fixed point theory. Thus, in the single-valued case, the existence of a unique solution is proved by using the classical Banach fixed point theorem while an existence result is established via Krasnosel’skiĭ’s fixed point theorem. The Leray–Schauder nonlinear alternative for multi-valued maps is the basic tool to prove an existence result in the multi-valued case. Finally, our results are well illustrated by numerical examples.

Nonlocal Sequential Boundary Value Problems for Hilfer Type Fractional Integro-Differential Equations and Inclusions

In the present research, we study boundary value problems for fractional integro-differential equations and inclusions involving the Hilfer fractional derivative. Existence and uniqueness results are obtained by using the classical fixed point theorems of Banach, Krasnosel’skiĭ, and Leray–Schauder in the single-valued case, while Martelli’s fixed point theorem, a nonlinear alternative for multivalued maps, and the Covitz–Nadler fixed point theorem are used in the inclusion case. Examples are presented to illustrate our results.

Existence results for coupled system of nonlinear differential equations and inclusions involving sequential derivatives of fractional order

<abstract><p>In this article, we investigate new results of existence and uniqueness for systems of nonlinear coupled differential equations and inclusions involving Caputo-type sequential derivatives of fractional order and along with new kinds of coupled discrete (multi-points) and fractional integral (Riemann-Liouville) boundary conditions. Our investigation is mainly based on the theorems of Schaefer, Banach, Covitz-Nadler, and nonlinear alternatives for Kakutani. The validity of the obtained results is demonstrated by numerical examples.</p></abstract>

On multi-term proportional fractional differential equations and inclusions

The aim of this paper is to study new nonlocal boundary value problems of fractional differential equations and inclusions supplemented with slit-strips integral boundary conditions. Based on the functional analysis tools, the existence results for a nonlinear boundary value problem involving a proportional fractional derivative are presented. In addition to that, the extension of the problem at hand to its inclusion case is discussed. The obtained results are very interesting and are well illustrated with examples.

Ivanov’s Theorem for Admissible Pairs Applicable to Impulsive Differential Equations and Inclusions on Tori

The main aim of this article is two-fold: (i) to generalize into a multivalued setting the classical Ivanov theorem about the lower estimate of a topological entropy in terms of the asymptotic Nielsen numbers, and (ii) to apply the related inequality for admissible pairs to impulsive differential equations and inclusions on tori. In case of a positive topological entropy, the obtained result can be regarded as a nontrivial contribution to deterministic chaos for multivalued impulsive dynamics.