and Applied Analysis 3 Lemma 1.4 see 2 . Let X ⊃ φ be a BK-space and Y any of the spaces c0, c, or ∞. If A ∈ X,Y , then ‖LA‖ ‖A‖ X, ∞ sup n ‖An‖X < ∞, 1.4 where ‖A‖ X, ∞ denotes the operator norm for the matrix A ∈ X, ∞ . Sargent 3 defined the following sequence spaces. Let C denote the space whose elements are finite sets of distinct positive integers. Given any element σ of C, we denote by c ...

The main goal of this study is to demonstrate an existence result a coupled implicit Riemann-Liouville fractional integral equation. First, we prove new fixed point theorem in spaces with extended norm structure. That generalized Darbo’s associated the vector Kuratowski measure noncompactness. Second, employ our obtained investigate solutions equation on Banach space C([0,1],R)×C([0,1],R).

Using the techniques of measures of noncompactness and Darbo fixed point theorem, we present some existence results for solutions of systems of nonlinear equations in Banach spaces. Also, as an application, we discuss the existence of solutions for a general system of nonlinear functional integral equations, which extends some previous results in the literature. An example is given to show the ...

In the present paper, concept of almost periodic waves is introduced to discontinuous impulsive fractional inclusions involving Caputo derivative. New results on existence and uniqueness are established by using theory operator semigroups, Hausdorff measure noncompactness, fixed point theorems calculus techniques. Applications a class fractional-order gene regulatory network (GRN) models propos...

and Applied Analysis 3 Definition 2 (see [3]). The Caputo fractional derivative of order q > 0 with the lower limit zero for a function u is defined as C D q t u (t) = 1 Γ (n − q) ∫ t 0 (t − s) n−q−1 u (n) (s) ds, t > 0, 0 ≤ n − 1 < q < n, (8) where the function u(t) has absolutely continuous derivatives up to order n − 1. If u is an abstract function with values in E, then the integrals which ...

In this manuscript, we examine both the existence and stability of solutions boundary value problems Hadamard-type fractional differential equations variable order. New outcomes are obtained in paper based on Darbo’s fixed point theorem (DFPT) combined with Kuratowski measure noncompactness (KMNC). We construct an example to illustrate validity observed results.

Abstract This work is to analyze a nonlocal dispersal model governed by Volterra type integral and two space integrals. A weighted included, an existence result of solutions for this proved. We assume suitably Hartman-type sign condition use sufficiently regular measure noncompactness. Finally, the degree theory referring condensing operators applied.

Using the techniques of some new measures of noncompactness we prove in this paper some existence theorems concerning the global attractivity and ultimate positivity of the solutions for a nonlinear functional integral equation. Our investigations are placed in the Banach space of real-valued functions defined, continuous and bounded on unbounded intervals together with the applications of a re...