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This paper aims to investigate the existence of solution of a generalized Hadamard proportional fractional integral equations involving non-singular kernels. First, we introduce Hadamard fractional integral equations. Then, we demonstrate the existence of the solution of Hadamard proportional fractional integral equations based on the concept of a measure of noncompactness and Petryshyn's fixed point theorem. After that, we provide suitable examples which evidence the existing result. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to consider the fractional delayed evolution equation of order γ ∈ (1 , 2) in ordered Banach space. In the absence of assumptions about the compactness of cosine families or related sine families, the existence results of positive solutions are studied by using some fixed point theorems and monotone iterative method under the conditions that nonlinear function satisfies the non-compactness measure conditions and some appropriate growth conditions or order conditions. [ABSTRACT FROM AUTHOR]

In this work, we show the existence of solutions for a higher order implicit fractional differential equations with multi-point boundary conditions at resonance. Our results are obtained by utilizing the (Kuratovski) measure of non-compactness and abstract continuation theorem for k-set contractions. Finally, an example is given to illustrate the applicability of theoretical result. [ABSTRACT FROM AUTHOR]

We study the long time behavior of solutions for time-fractional pseudo-parabolic equations involving time-varying delays and nonlinear pertubations, where the nonlinear term is allowed to have superlinear growth. Concerning the associated linear problem, we establish a variation-of-parameters formula of mild solutions and prove some regularity estimates of resolvent operators. In addition, thanks to local estimates on Hilbert scales, fixed point arguments and a new Halanay type inequality, we obtain some results on the global solvability, stability, dissipativity and the existence of decay solutions to our problem. [ABSTRACT FROM AUTHOR]

This study aims to resolve weighted fractional operators of variable order in specific spaces. We establish an investigation on a boundary value problem of weighted fractional derivative of one function with respect to another variable order function. It is essential to keep in mind that the symmetry of a transformation for differential equations is connected to local solvability, which is synonymous with the existence of solutions. As a consequence, existence requirements for weighted fractional derivative of a function with respect to another function of constant order are necessary. Moreover, the stability with in Ulam–Hyers–Rassias sense is reviewed. The outcomes are derived using the Kuratowski measure of non-compactness. A model illustrates the trustworthiness of the observed results. [ABSTRACT FROM AUTHOR]

We study the existence of decay solutions for a class of abstract fractional mobile-immobile equations involving impulses and nonlinear perturbations in Hilbert spaces, where the nonlinear terms are supposed to be of superlinear growth. Concerning the associated linear problem, we make use of the theory of completely positive functions to establish a variation of parameters formula in terms of the relaxation functions and to prove the differentiability of resolvent families. In addition, based on local estimates on Hilbert scales and fixed point arguments, we obtain some results on the global existence and the existence of a compact set of decay solutions to our problem. [ABSTRACT FROM AUTHOR]

In this paper, we discuss fixed point theorems for a new χ-set contraction condition in partially ordered Banach spaces, whose positive cone K is normal, and then proceed to prove some coupled fixed point theorems in partially ordered Banach spaces. We relax the conditions of a proper domain of an underlying operator for partially ordered Banach spaces. Furthermore, we discuss an application to the existence of a local fractional integral equation. [ABSTRACT FROM AUTHOR]

In this work, we introduce the concepts of multivariate generalized Meir–Keeler condensing operator, and multivariate L-function and prove some new fixed point theorems with the aid of the measure of non-compactness. Our results generalize and extend a lot of comparable results in the literature. Also, we use these results to discuss the solvability for a system of functional integral equations of Volterra type in three variables. Finally, we present an example to support our results. [ABSTRACT FROM AUTHOR]

In this paper, by using the cosine family theory, measure of non-compactness and the generalization of Darbo-fixed point theorem, we establish the existence of mild solutions of nonlinear second-order impulsive integro-differential evolution equations of Volterra type in Banach spaces. The result obtained herein generalizes and improves some known results. [ABSTRACT FROM AUTHOR]

In this paper, we show that every infinite dimensional Banach space admits a homogenous measure of non-compactness not equivalent to the Hausdorff measure. Therefore, it resolves a long-standing question. [ABSTRACT FROM AUTHOR]

We prove the existence and finite-time attractivity of solutions to semilinear tempered fractional wave equations with sectorial operator and superlinear nonlinearity. Our analysis is based on the α-resolvent theory, the fixed point theory for condensing maps and the local estimates of solutions. An application to a class of partial differential equations will be given. [ABSTRACT FROM AUTHOR]

There are many forms of solutions that occur obviously, and in various situations one cannot just switch to one of them and establish solutions in that sense. It is valuable to study solutions with strong differentiability properties, but it might be difficult to confirm their existence. Therefore, one essentially considers solutions in a weaker sense. In this note, we establish the existence of monotone solutions of the dynamic system of the bacterial growth of iterative fractional differential equations, found by a new coupled and triple fixed point theorem in the sense of Darbo processing. We propose these theorems (Darbo type) for a new contraction by using a measure of non-compactness in Banach spaces. The new outcomes show some special well-known recent results. [ABSTRACT FROM AUTHOR]

We prove the global solvability and weakly asymptotic stability for a semilinear fractional differential inclusion subject to impulsive effects by analyzing behavior of its solutions on the half-line. Our analysis is based on a fixed point principle for condensing multi-valued maps, which is employed for solution operator acting on the space of piecewise continuous functions. The obtained results will be applied to a lattice fractional differential system. [ABSTRACT FROM AUTHOR]

In this paper, the concept of contraction via the measure of non-compactness on a Banach space is investigated by generalizing some results which have been previously discussed in literatures. Furthermore, to validity of the theorems and homotopy perturbation method (HPM), as a technical solution, they are applied on some nonlinear singular integral equations. [ABSTRACT FROM AUTHOR]

We show that every measure of non-compactness on a W*-algebra is an ideal F-pseudonorm. We establish a criterion of the right Fredholm property of an element with respect to a W*-algebra. We prove that the element − I realizes the maximum distance from a positive element to a subset of all isometries of a unital C*-algebra, here I is the unit of the C*-algebra. We also consider differences of two finite products of elements from the unit ball of a C*-algebra and obtain an estimate of their ideal F-pseudonorms. We conclude the paper with a convergence criterion in complete ideal F-norm for two series of elements from a W*-algebra. [ABSTRACT FROM AUTHOR]

A characterization of a weight $$v$$ governing the boundedness/compactness of the weighted kernel operator $$K_v$$ in variable exponent Lebesgue spaces $$L^{p(\cdot )}$$ is established under the log-Hölder continuity condition on exponents of spaces. The kernel operator involves, for example, weighted variable parameter fractional integral operators. The distance between $$K_v$$ and the class of compact integral operators acting from $$L^{p(\cdot )}$$ to $$L^{q(\cdot )}$$ (measure of non-compactness) is also estimated from above and below. [ABSTRACT FROM AUTHOR]

This paper concerns with the IVP for set differential equations involving causal operators with memory. By using the techniques of the measure of non-compactness, the existence of solutions has been established. The maximal and minimal solutions are obtained by means of Arzela-Ascoli Theorem. [ABSTRACT FROM AUTHOR]

We study the control systems governed by abstract Volterra equations without uniqueness in a Banach space. By using the technique of the theory of condensing maps and multivalued analysis tools, we obtain the existence result, investigate the topological structure of the solution set, and prove the invariance of a reachability set of the control system under nonlinear perturbations. Examples concerning fractional order differential equations and first order evolution equations with multiple delays are proposed to demonstrate the applications to approximate controllability results. [ABSTRACT FROM AUTHOR]

In this paper, by using the cone theory and monotone iterative technique, we investigate the existence of extremal solutions and unique solution of the integral boundary value problem for a class of first-order impulsive integro-differential equations in a real Banach space. An explicit iterative scheme for the unique solution and an error estimate of the approximation sequence are also derived. [ABSTRACT FROM AUTHOR]

The measure of non–compactness is estimated from below for various operators, including the Hardy–Littlewood maximal operator, the fractional maximal operator and the Hilbert transform, all acting between weighted Lebesgue spaces. The identity operator acting between weighted Lebesgue spaces and also between the counterparts of these spaces with variable exponents is similarly analysed. These results enable the lack of compactness of such operators to be quantified. [ABSTRACT FROM AUTHOR]

The Mönch fixed point theorem and the corresponding continuation theorem of Leray-Schauder type for admissible set-valued maps defined on Fréchet spaces is proved. The most conceivably simplistic definition of condensing set-valued maps in terms of functional relation, which binds an MNC of the image of a subset under the operator with the measure of that set, is given. This approach generalizes in particular the Sadovskiĭ and Darbo theorems beyond many other results contained in the literature of the subject. [ABSTRACT FROM AUTHOR]