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A note on the measure of solvability

100%

Caponetti D. , Trombetta G.

tom Vol. 52, nr 2

179-183

Let X be an infinite-dimensional Banach space. The measure of solvability v(I) of the identity operator I is equal to 1.

On the hybrid Caputo-proportional fractional differential inclusions in Banach spaces

100%

Abbas M. I.

Journal of Mathematics and Applications

2022

tom Vol. 45

5--20

The current article concerns an existence criteria of solutions of nonlinear fractional differential inclusions in the sense of the hybrid Caputo-proportional fractional derivatives in Banach space. The investigation of the main result relies on the set-valued issue of Mönch fixed point theorem incorporated with the Kuratowski measure of non-compactness.

On some qualitative properties of integrable solutions for Cauchy-type problem of fractional order

84%

Metwali M. M. A.

Journal of Mathematics and Applications

2017

tom Vol. 40

121--p134

The paper discusses the existence of solutions for Cauchy-type problem of fractional order in the space of Lebesgue integrable functions on bounded interval. Some qualitative properties of solutions are presented such as monotonicity, uniqueness and continuous dependence on the initial data. The main tools used are measure of weak (strong) noncompactness, Darbo fixed point theorem and fractional calculus.

Generalizations of Darbo’s fixed point theorem for new condensing operators with application to a functional integral equation

84%

Rehman H. u. , Gopal D. , Kumam P.

Demonstratio Mathematica

2019

tom Vol. 52, nr 1

166--182

In this paper, we provide some generalizations of the Darbo’s fixed point theorem associated with the measure of noncompactness and present some results on the existence of the coupled fixed point theorems for a special class of operators in a Banach space. To acquire this result, we define α-ψ and β-ψ con-densing operators and using them we propose new fixed point results. Our results generalize and extendsome comparable results from the literature. Additionally, as an application, we apply the obtained fixedpoint theorems to study the nonlinear functional integral equations.

Measure of noncompactness and neutral functional differential equations with state-dependent delay

67%

Benchohra M. , Henderson J. , Medjadj I.

Journal of Mathematics and Applications

2016

tom Vol. 39

23--45

Our aim in this work is to study the existence of solutions of first and second order for neutral functional differential equations with state-dependent delay. We use the Mönch’s fixed point theorem for the existence of solutions and the concept of measures of noncompactness.