Existence of nondecreasing solutions of some nonlinear integral equations of fractional order

Volume 8, Issue 6, pp 1112--1126 http://dx.doi.org/10.22436/jnsa.008.06.20

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Authors

Ümit Çakan - Fen Edebiyat Fakültesi, Matematik Bolümü, Nevsehir Haci Bektas Veli Üniversitesi, Nevsehir, 50300, Turkey. İsmet Özdemir - Eğitim Fakültesi, İnönü Üniversitesi, A-Blok, Malatya, 44280, Turkey.

Abstract

The purpose of this paper is to examine the class of functional integral equations of fractional order in the space of continuous functions on interval \([0; a]\) : Using Darbo's fixed point theorem associated with the measure of noncompactness, we present sufficient conditions for existence of nondecreasing solutions of some functional integral equations of fractional order. These existence results include several obtained from previous studies. Finally, we establish some examples to show that our results are applicable.

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Keywords

• Nonlinear integral equations
• measure of noncompactness
• nondecreasing solution
• Darbo fixed point theorem
• Riemann-Liouville fractional integral.

MSC

•  26A33
•  45M99
•  47H08
•  47H10

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