In the current contribution, an appropriate quantity connected to space of all convergent sequences is provided and shown be a measure noncompactness in Banach space. Through application fixed point theorems Darbo Meir–Keeler, this amount used discuss whether solution infinite system fractional Sturm–Liouville operators exists. We offer numerical example as key finding study.

The current article discusses the existence of monotonic discontinuous solutions for general nonlinear quadratic Volterra-Urysohn functional-integral equations in Orlicz spaces E? when function ? satisfies ?2-condition. case Lebesgue Lp (p > 1) are also examined. We use arguments measure noncompactness with Darbo fixed point theorem to prove our results.

This paper is devoted to the existence of solutions for certain classes nonlinear sequential Caputo and Caputo-Hadamard fractional differential equations with Dirichlet boundary conditions in Banach spaces. Moreover, our analysis based on Darbo’s fixed point theorem conjunction technique Hausdorff measure noncompactness. An example also presented illustrate effectiveness main results.

This study focused on the approximate controllability results for Hilfer fractional delay evolution equations of Sobolev type without uniqueness. Initially, Lipschitz condition is derived from hypothesis, which represented by a measure noncompactness, in particular, nonlinearity. We also examined continuity solution map equation and topological structure set. Furthermore, we prove with delay. F...

In this article, we study the existence of a solution to mixed hybrid fractional differential equations sequential type with nonlocal integral boundary conditions. The main results are established aid Darbo’s fixed point theorem and Hausdorff’s measure noncompactness method. stability proposed equation is also investigated using Ulam–Hyer technique. addition, an applied example that supports th...

The main purpose of this study is to introduce the absolute Lucas series spaces and investigate their some algebraic topological structure such as inclusion relations, $BK-$ space, duals Schauder basis. Also, characterizations matrix operators related these space with norms are given. Finally, by using Hausdorff measure noncompactness, necessary sufficient conditions for a operator on them be c...

whenever the series are convergent for all n≥ 1. For any given subsets X , Y of s, we will say that the operator represented by the infinite matrix A = (anm)n,m≥1 maps X into Y that is A∈ (X ,Y), if (i) the series defined by An(x)= ∑∞ m=1 anmxm are convergent for all n≥ 1 and for all x ∈ X ; (ii) Ax ∈ Y for all x ∈ X . If c ⊂ cA = {x : Ax ∈ c},A is conservative. Well-known necessary and suffici...