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Volume 12
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

New Extension of Darbo’s Fixed Point Theorem and Its Application to a System of Weighted-Fractional-Type Integral Equations

by
Marija Paunović
1,2,
Ana Savić
3,
Hemanta Kalita
4,
Sudip Deb
5 and
Vahid Parvaneh
6,*
1
Department of Natural Sciences, Faculty of Hotel Management and Tourism, University of Kragujevac, 36210 Vrnjačka Banja, Serbia
2
Faculty of Business and Law, University ”MB”, 11000 Belgrade, Serbia
3
Academy of Technical and Art Applied Studies, 11000 Belgrade, Serbia
4
Mathematics Division, School of Advanced Sciences and Languages, VIT Bhopal University, Bhopal-Indore Highway, Sehore 466114, Madhya Pradesh, India
5
Department of Mathematics, Pandit Deendayal Upadhyaya Adarsha Mahavidyalaya, Amjonga, Goalpara 783124, Assam, India
6
Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb 6787141343, Iran
*
Author to whom correspondence should be addressed.
Mathematics 2024, 12(13), 2133; https://doi.org/10.3390/math12132133 (registering DOI)
Submission received: 30 May 2024 / Revised: 28 June 2024 / Accepted: 5 July 2024 / Published: 7 July 2024
(This article belongs to the Special Issue Soft Computing and Fuzzy Mathematics: New Advances and Applications)
Versions Notes

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. In applying our new extensions, we prove the existence of solutions to a system of weighted fractional types of integral equations in Banach space BC(R+). At the end, we establish an example to show the applicability of our discovery.
Keywords: fractional integral equation (F.I.E.); measure of noncompactness (M.N.C.); fixed point theorem (F.P.T.); Darbo’s fixed point theorem (D.F.P.T.) fractional integral equation (F.I.E.); measure of noncompactness (M.N.C.); fixed point theorem (F.P.T.); Darbo’s fixed point theorem (D.F.P.T.)

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MDPI and ACS Style

Paunović, M.; Savić, A.; Kalita, H.; Deb, S.; Parvaneh, V. New Extension of Darbo’s Fixed Point Theorem and Its Application to a System of Weighted-Fractional-Type Integral Equations. Mathematics 2024, 12, 2133. https://doi.org/10.3390/math12132133

AMA Style

Paunović M, Savić A, Kalita H, Deb S, Parvaneh V. New Extension of Darbo’s Fixed Point Theorem and Its Application to a System of Weighted-Fractional-Type Integral Equations. Mathematics. 2024; 12(13):2133. https://doi.org/10.3390/math12132133

Chicago/Turabian Style

Paunović, Marija, Ana Savić, Hemanta Kalita, Sudip Deb, and Vahid Parvaneh. 2024. "New Extension of Darbo’s Fixed Point Theorem and Its Application to a System of Weighted-Fractional-Type Integral Equations" Mathematics 12, no. 13: 2133. https://doi.org/10.3390/math12132133

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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