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1
Content available On the hybrid Caputo-proportional fractional differential inclusions in Banach spaces
Abbas Mohamed I.
Journal of Mathematics and Applications
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2022
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Vol. 45
5--20
EN
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.
2
Content available remote Generalizations of Darbo’s fixed point theorem for new condensing operators with application to a functional integral equation
Rehman Habib ur, Gopal Dhananjay, Kumam Poom
Demonstratio Mathematica
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2019
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Vol. 52, nr 1
166--182
EN
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.
3
Content available remote Characterizations of compact operators on ℓp-type fractional sets of sequences
Özger Faruk
Demonstratio Mathematica
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2019
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Vol. 52, nr 1
105--115
EN
Among the sets of sequences studied, difference sets of sequences are probably the most common type of sets. This paper considers some ℓp-type fractional difference sets via the gamma function. Although, we characterize compactness conditions on those sets using the main key of Hausdorff measure of noncompactness, we can only obtain sufficient conditions when the final space is ℓ∞. However, we use some recent results to exactly characterize the classes of compact matrix operators when the final space is the set of bounded sequences.
4
Content available On some qualitative properties of integrable solutions for Cauchy-type problem of fractional order
Metwali M. M. A.
Journal of Mathematics and Applications
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2017
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Vol. 40
121--p134
EN
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.
5
Content available Measure of noncompactness and neutral functional differential equations with state-dependent delay
Benchohra M., Henderson J., Medjadj I.
Journal of Mathematics and Applications
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2016
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Vol. 39
23--45
EN
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.
6
Content available On the solutions of a class of nonlinear functional integral quations in space C [0,a]
Özdemir İ., Çakan Ü.
Journal of Mathematics and Applications
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2015
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Vol. 38
105--114
EN
The principal aim of this paper is to give sufficient conditions for solvability of a class of some nonlinear functional integral equations in the space of continuous functions defined on interval [0,a]. The main tool used in our study is associated with the technique of measures of noncompactness. We give also some examples satisfying the conditions of our main theorem but not satisfying the conditions in [8].
7
Content available remote A note on the measure of solvability
Caponetti D., Trombetta G.
Bulletin of the Polish Academy of Sciences. Mathematics
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2004
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Vol. 52, nr 2
179-183
EN
Let X be an infinite-dimensional Banach space. The measure of solvability v(I) of the identity operator I is equal to 1.
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