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.

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...

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...

in this paper, using the tools involving measures of noncompactness and darbo fixed point theorem forcondensing operator, we study the existence of solutions for a large class of generalized nonlinear quadraticfunctional integral equations. also, we show that solutions of these integral equations are locally attractive.furthermore, we present an example to show the efficiency and usefulness of ...

*Correspondence: [email protected] 1Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia 2Department of Mathematics, Aligarh Muslim University, Aligarh, 202 002, India Abstract In this paper, we characterize the matrix classes ( 1, p(F)) (1≤ p <∞), where p(F) is some Fibonacci di...

We study a controllability problem for a system governed by a semilinear functional differential inclusion in a Banach space in the presence of impulse effects and delay. Assuming a regularity of the multivalued non-linearity in terms of the Hausdorff measure of noncompactness we do not require the compactness of the evolution operator generated by the linear part of inclusion. We find existenc...

Abstract: In this paper existence of mild solution of a class of second order partial neutral differential equation with state dependent delay and non-instantaneous impulses is investigated. Hausdorff measure of noncompactness and Darbo Sadovskii fixed point theorem are used to prove the existence. Also, some restrictive conditions such as the compactness assumption on the associated cosine or ...

in this work are studied the jacobians of certain singular transformations and the corresponding measures which support the jacobian computations.

In this paper we introduce a parameter ω∞ in the space of functions L0. The parameter measures the lack of equimeasurability using a sequence of functions which controls the oscillations of every function of a given subset of L0. We estimate the Hausdorff measure of noncompactness in terms of ω∞ and the parameter σ (see [3]) and characterize the totally bounded subsets of L0. A criterion of com...