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

Marija Paunović, Ana Savić, Hemanta Kalita, Sudip Deb and Vahid Parvaneh ()
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Marija Paunović: Department of Natural Sciences, Faculty of Hotel Management and Tourism, University of Kragujevac, 36210 Vrnjačka Banja, Serbia
Ana Savić: Academy of Technical and Art Applied Studies, 11000 Belgrade, Serbia
Hemanta Kalita: Mathematics Division, School of Advanced Sciences and Languages, VIT Bhopal University, Bhopal-Indore Highway, Sehore 466114, Madhya Pradesh, India
Sudip Deb: Department of Mathematics, Pandit Deendayal Upadhyaya Adarsha Mahavidyalaya, Amjonga, Goalpara 783124, Assam, India
Vahid Parvaneh: Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb 6787141343, Iran

Mathematics, 2024, vol. 12, issue 13, 1-15

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 in Banach space B C ( 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 ) (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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