fixed-point theorem

In this work,  we are interested in representing the solution of Hadamard type fractional differential equation by introducing the concept of double sequence space $2^c(\Delta)$.  After that, we construct the Hausdorff measure of non-compactness on the space $2^c(\Delta)$.  Furthermore,  we see the existence of a solution of Hadamard-type fractional differential equation on the space $2^c(\Delta)$. After that, we demonstrate an example to see the applicability of our results.

The objective of this work is to investigate the existence and uniqueness of the solution to a nonlinear fractional integro-differential equation with a non-local condition involving the generalized fractional proportional Caputo derivative of two distinct orders. To achieve this, Krasnoselskii’s fixed point theorem is utilized to examine the existence of the solution, followed by the application of Banach’s fixed point theorem to study the uniqueness. Lastly, two illustrative examples are provided to highlight the main results.

‎This article provides the presence of solutions to a fractional functional integro-differential equation via measures of non-compactness‎. ‎We present and prove a novel theorem that guarantees the existence of solutions‎, ‎employing Petryshyn's fixed point theorem in the space of continuous functions‎. ‎These findings build upon previous studies by establishing the existence of results under less stringent conditions‎. ‎Furthermore‎, ‎we provide illustrative examples of such equations to showcase the efficacy of the obtained results.

In this paper, by using the techniques of measures of non-compactness and the Petryshyn fixed point theorem, we investigate the existence of solutions of a Caputo fractional functional integro-differential equation and obtain some new results. These existing results involve particular results gained from earlier studies under weaker conditions.

In this manuscript, we study the existence of mild solutions to initial value problems for hybrid fractional semi-linear evolution equations. On the other hand, we prove four different types of Ulam-Hyers stability results for mild solutions. The existence of mild solutions is proved by the Dhage fixed point theorem. Finally, an example is given to illustrate our results.

This paper explores the study of a specific category of nonlinear multi-point boundary value problems (BVPs) associated with Riesz-Caputo fractional differential equations and integral boundary conditions. The primary objective is to establish the existence of solutions under specific assumptions. We use Krasnoselskii's fixed point theorem and Leray-Schauder's nonlinear alternative to achieve this goal. Furthermore, numerical examples are presented and plotted to demonstrate the effectiveness of the obtained results.

The purpose of this paper is to analyze the solvability of a class of stochastic functional integral equations by utilizing the measure of non-compactness with Petryshyn’s fixed point theorem in a Banach space. The results obtained in this paper cover numerous existing results concluded under some weaker conditions by many authors. An example is given to support our main theorem.

The main aim of this study is to prove the stability and hyperstability of multi-Euler-Lagrange additive mappings in the setting of intuitionistic fuzzy normed spaces by an alternative fixed point theorem.

In this paper, the existence, uniqueness, compactness, and stability of a coupled random differential equations involving the Hilfer fractional derivatives with nonlocal boundary conditions are discussed. Arguments are discussed via some random fixed point theorems in a separable vector Banach spaces and Ulam type stability. Some examples are presented to ensure the abstract results.

Here, we investigate the existence of solutions for the initial value problem of fractional-order differential inclusion containing a nonlocal infinite-point or Riemann–Stieltjes integral boundary conditions. A sufficient condition for the uniqueness of the solution is given. The continuous dependence of the solution on the set of selections and on some data is studied. At last, examples are designed to illustrate the applicability of the theoretical results.

In this paper, the existence of the solutions of a class of weakly singular integral equations in Banach algebra is investigated. ‎The basic tool used in investigations is the technique of the measure of non-compactness and Petryshyn’s fixed point theorem. Also, for the applicability of the obtained results, some examples are given.

This work studies the existence and the uniqueness of the solution to a kind of high-order nonlinear fractional integro-differential equations involving Rieman-Liouville fractional derivative. The boundary condition is of integral type which entangles ending point of the domain. First, the unique exact solution is extracted in terms of Green's function for the linear fractional differential equation and then Banach contraction mapping theorem is applied to prove the main result in the case of general nonlinear source term. Furthermore, our main result is demonstrated by an illustrative example to show its legitimacy and applicability.

This research inscription gets to grips with a novel type of boundary value problem of nonlinear differential equations encapsuling a fractional derivative known as the Hadamard fractional operator. Our results rely on the standard tools of functional analysis. The existence of the solutions of the aforehand equations is tackled by using Schaefer and Krasnoselskii's fixed point theorems, whereas their uniqueness is handled using the Banach fixed point theorem. Two pertinent examples are presented to point out the applicability of our main results.

In this study, we focus on the existence of a solution for a fractional differential system with integral boundary conditions in specific fractional derivative Banach space. We establish the existence of a solution by using the Schauder fixed point theorem.

In this paper, we have introduced a computational method for a class of two-dimensional nonlinear Volterra integral equations, based on the expansion of the solution as a series of Haar functions. To achieve this aim it is necessary to define the integral operator. The Banach fixed point theorem guarantees that under certain assumptions this operator has a unique fixed point, we have introduced an orthogonal projection and by interpolation property, we have achieved an operational matrix of integration. Also, by using the Banach fixed point theorem, we get an upper bound for the error of our method. Since our examples in this article are selected from different references, so should be the numerical results obtained here can be compared with other numerical methods.

Hilfer-Katugampola-type fractional stochastic differential equations with nonlocal conditions are considered in this paper. By using the fixed point theorem, the existence and uniqueness of solutions for the considered problem are proved. Ulam-Hyers stability for the considered problem is studied. Finally, an example is presented to show our main results.

This work elucidates the sufficient conditions for establishing some existence and uniqueness results for a Musca Domestica model that is governed by a first-order nonlinear differential equation with iterative terms resulting from a time and state-dependent delay. The existence of at least one positive periodic solution is proved by using Schauder's fixed point theorem with the help of some properties of an obtained Green's function. Furthermore, under an additional condition, the Banach contraction principle is applied to guarantee the existence, uniqueness and stability of solutions. Finally, the validity of our main findings is demonstrated by two examples. Our findings are completely new and generalize previous ones to some degree.

The aim of this manuscript is to introduce the concept of intuitionistic fuzzy $b$-metric-like spaces and discuss some fixed point results to certify the existence and uniqueness of a fixed point. Non-trivial examples are imparted to illustrate the viability of the proposed method.

In this paper, we investigate a class of initial value problems of nonlinear fractional differential equations with state deviating arguments, delayed impulses and supremum on the half line. A global existence-uniqueness result is obtained using the theory of fixed points in uniform spaces, which is different from what is commonly used in such studies. Our result is obtained in a setting where classical variants of the fixed point theorems frequently used in the literature are inapplicable, and moreover without any bounding restriction with respect to time, neither on the solution nor on the reaction part of the problem. Two examples illustrating our main findings are also given.

In this paper, we prove the existence and uniqueness of the solutions for a non-integer high order boundary value problem which is subject to the Caputo fractional derivative. The boundary condition is a non-local type. Analytically, we introduce the fractional Green’s function. The main principle applied to simulate our results is the Banach contraction fixed point theorem. We deduce this paper by presenting some illustrative examples. Furthermore, it is presented a numerical based semi-analytical technique to approximate the unique solution to the desired order of precision.