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Keywords = Darbo–Sadovskii fixed-point theorem

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11 pages, 233 KB  
Article
On Darbo- and Sadovskii-Type Fixed Point Theorems in Banach Spaces
by Leszek Olszowy and Tomasz Zając
Symmetry 2024, 16(4), 392; https://doi.org/10.3390/sym16040392 - 27 Mar 2024
Cited by 4 | Viewed by 1339
Abstract
The paper aims to generalize several known Darbo- and Sadovskii-type fixed point theorems. These generalizations weaken the assumptions used so far. In addition, an example of an application is presented. Full article
18 pages, 432 KB  
Article
A New Result Concerning Nonlocal Controllability of Hilfer Fractional Stochastic Differential Equations via almost Sectorial Operators
by Sivajiganesan Sivasankar, Ramalingam Udhayakumar, Muchenedi Hari Kishor, Sharifah E. Alhazmi and Shrideh Al-Omari
Mathematics 2023, 11(1), 159; https://doi.org/10.3390/math11010159 - 28 Dec 2022
Cited by 13 | Viewed by 2099
Abstract
This manuscript mainly focused on the nonlocal controllability of Hilfer fractional stochastic differential equations via almost sectorial operators. The key ideas of the study are illustrated by using ideas from fractional calculus, the fixed point technique, and measures of noncompactness. Then, the authors [...] Read more.
This manuscript mainly focused on the nonlocal controllability of Hilfer fractional stochastic differential equations via almost sectorial operators. The key ideas of the study are illustrated by using ideas from fractional calculus, the fixed point technique, and measures of noncompactness. Then, the authors establish new criteria for the mild existence of solutions and derive fundamental characteristics of the nonlocal controllability of a system. In addition, researchers offer theoretical and real-world examples to demonstrate the effectiveness and suitability of our suggested solutions. Full article
(This article belongs to the Special Issue Fractional Calculus and Mathematical Applications)
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