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Keywords = measure of noncompactness ( M N C )

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15 pages, 280 KiB  
Article
New Extension of Darbo’s Fixed Point Theorem and Its Application to a System of Weighted-Fractional-Type Integral Equations
by Marija Paunović, Ana Savić, Hemanta Kalita, Sudip Deb and Vahid Parvaneh
Mathematics 2024, 12(13), 2133; https://doi.org/10.3390/math12132133 - 7 Jul 2024
Cited by 1 | Viewed by 1033
Abstract
In this article, we introduce several new extensions of Darbo’s fixed point theorem with newly constructed contraction functions associated with the measure of noncompactness. We apply our new extensions to prove the existence of solutions for a system of weighted fractional integral equations [...] Read more.
In this article, we introduce several new extensions of Darbo’s fixed point theorem with newly constructed contraction functions associated with the measure of noncompactness. We apply our new extensions to prove the existence of solutions for a system of weighted fractional integral equations in Banach space BC(R+). At the end, we establish an example to show the applicability of our discovery. Full article
(This article belongs to the Special Issue Soft Computing and Fuzzy Mathematics: New Advances and Applications)
18 pages, 354 KiB  
Article
Existence of Hilfer Fractional Stochastic Differential Equations with Nonlocal Conditions and Delay via Almost Sectorial Operators
by Sivajiganesan Sivasankar, Ramalingam Udhayakumar, Velmurugan Subramanian, Ghada AlNemer and Ahmed M. Elshenhab
Mathematics 2022, 10(22), 4392; https://doi.org/10.3390/math10224392 - 21 Nov 2022
Cited by 8 | Viewed by 2146
Abstract
In this article, we examine the existence of Hilfer fractional (HF) stochastic differential systems with nonlocal conditions and delay via almost sectorial operators. The major methods depend on the semigroup of operators method and the Mo¨nch [...] Read more.
In this article, we examine the existence of Hilfer fractional (HF) stochastic differential systems with nonlocal conditions and delay via almost sectorial operators. The major methods depend on the semigroup of operators method and the Mo¨nch fixed-point technique via the measure of noncompactness, and the fundamental theory of fractional calculus. Finally, to clarify our key points, we provide an application. Full article
(This article belongs to the Special Issue Fractional Calculus and Nonlinear Systems)
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