Hilfer–Hadamard Fractional Boundary Value Problems with Nonlocal Mixed Boundary Conditions

This paper is concerned with the existence and uniqueness of solutions for a Hilfer–Hadamard fractional differential equation, supplemented with mixed nonlocal (multi-point, fractional integral multi-order and fractional derivative multi-order) boundary conditions. The existence of a unique solution is obtained via Banach contraction mapping principle, while the existence results are established by applying the fixed point theorems due to Krasnoselskiĭ and Schaefer and Leray–Schauder nonlinear alternatives. We demonstrate the application of the main results by presenting numerical examples. We also derive the existence results for the cases of convex and non-convex multifunctions involved in the multi-valued analogue of the problem at hand.

Qualitative Analysis of some Types of Neutral Delay Differential Equations

In this paper, we conduct some qualitative analysis that involves the global asymptotic stability (GAS) of the Neutral Differential Equation (NDE) with variable delay, by using Banach contraction mapping theorem, to give some necessary conditions to achieve the GAS of the zero solution.

Stability analysis for a class of implicit fractional differential equations involving Atangana–Baleanu fractional derivative

Some fundamental conditions and hypotheses are established to ensure the existence, uniqueness, and stability to a class of implicit boundary value problems (BVPs) with Atangana–Baleanu–Caputo type derivative and integral. The required results are established by utilizing the Banach contraction mapping principle and fixed point theorem of Krasnoselskii. In addition, various types of stability results including Hyers–Ulam, generalized Hyers–Ulam, Hyers–Ulam–Rassias, and generalized Hyers–Ulam–Rassias stability are formulated for the problem under consideration. Pertinent examples are given to justify the results we obtain.

Solvability and stability of nonlinear hybrid ∆-difference equations of fractional-order

In this paper, we study a type of nonlinear hybrid Δ-difference equations of fractional-order. The main objective is to establish some stability criteria including the Ulam–Hyers stability, generalized Ulam–Hyers stability together with the Mittag-Leffler–Ulam–Hyers stability for the addressed problem. Prior to the stabilization processes, solvability criteria for the existence and uniqueness of solutions are considered. For this purpose, a hybrid fixed point theorem for triple operators and the Banach contraction mapping principle are applied, respectively. For the sake of illustrating the practical impact of the proposed theoretical criteria, we finish the paper with particular examples.

A Self-Adjoint Coupled System of Nonlinear Ordinary Differential Equations with Nonlocal Multi-Point Boundary Conditions on an Arbitrary Domain

The main object of this paper is to investigate the existence of solutions for a self-adjoint coupled system of nonlinear second-order ordinary differential equations equipped with nonlocal multi-point coupled boundary conditions on an arbitrary domain. We apply the Leray–Schauder alternative, the Schauder fixed point theorem and the Banach contraction mapping principle in order to derive the main results, which are then well-illustrated with the aid of several examples. Some potential directions for related further researches are also indicated.

Some Properties of Solutions to Multiterm Fractional Boundary Value Problems with p -Laplacian Operator

In this paper, we study some properties of positive solutions to a class of multipoint boundary value problems for nonlinear multiterm fractional differential equations with p -Laplacian operator. Using the Banach contraction mapping principle, the existence, the uniqueness, the positivity, and the continuous dependency on m -point boundary conditions of the solutions to the given problem are investigated. Also, two examples are presented to demonstrate our main results.

Existence and Approximation of Fixed Points of Enriched Contractions and Enriched φ-Contractions

We obtain existence and uniqueness fixed point theorems as well as approximation results for some classes of mappings defined by symmetric contractive type conditions in a convex metric space in the sense of Takahashi. By using a new approach, i.e., the technique of enrichment of contractive type mappings, we obtain general results which extend the well known Banach contraction mapping principle from metric spaces as well as other corresponding results for enriched mappings defined on Banach spaces. To indicate the relevance of our new results, we present some important particular cases and future directions of research.

Existence results to a ψ- Hilfer neutral fractional evolution equation with infinite delay

In this paper, we prove the existence and uniqueness of a mild solution to the system of ψ- Hilfer neutral fractional evolution equations with infinite delay H 𝔻0 αβ;ψ [x(t) − h(t, xt )] = A x(t) + f (t, x(t), xt ), t ∈ [0, b], b > 0 and x(t) = ϕ(t), t ∈ (−∞, 0]. We first obtain the Volterra integral equivalent equation and propose the mild solution of the system. Then, we prove the existence and uniqueness of solution by using the Banach contraction mapping principle and the Leray-Schauder alternative theorem.

EXISTENCE AND STABILITY ANALYSIS OF SOLUTIONS FOR FRACTIONAL LANGEVIN EQUATION WITH NONLOCAL INTEGRAL AND ANTI-PERIODIC-TYPE BOUNDARY CONDITIONS

In this paper, we deal with the existence and uniqueness (EU) of solutions for nonlinear Langevin fractional differential equations (FDE) having fractional derivative of different orders with nonlocal integral and anti-periodic-type boundary conditions. Also, we investigate the Hyres–Ulam (HU) stability of solutions. The existence result is derived by applying Krasnoselskii’s fixed point theorem and the uniqueness of result is established by applying Banach contraction mapping principle. An example is offered to ensure the validity of our obtained results.

Results of Positive Solutions for the Fractional Differential System on an Infinite Interval

The chief topic of this paper is to investigate the fractional differential system on an infinite interval. By introducing an appropriate compactness criterion in a special function space and applying the Schauder fixed-point theorem and the Banach contraction mapping principle, we established the results for the existence and uniqueness of positive solutions. An example is then given to show the utilization of the main results.