IJPAM: Volume 93, No. 3 (2014)

EXISTENCE THEOREM FOR AN INITIAL VALUE PROBLEM
OF FRACTIONAL ORDER IN $L_{1}\left( 0,1\right) $

Ibrahim Abouelfarag$^1$, Asmaa M. Awad$^2$
$^{1,2}$Mathematics Department
Faculty of Science
Suez Canal University
Ismailia, 41522, EGYPT
$^1$Mathematics Department
Faculty of Science and Education
Taif University
Al-Khurmah Branch, KINGDOM OF SAUDI ARABIA


Abstract. In this paper we study the existence of solution $x\in L_{1}\left( 0,1\right) $ for a functional integral equation. As an application we prove the existence of solution for an initial value problem of the fractional order. The main tools used are Schauder fixed point theorem, Lusin theorem and Scorza Dragoni theorem.

Received: November 6, 2013

AMS Subject Classification: 45G10

Key Words and Phrases: nonlinear functional integral equation, Fredholm operator, Volterra operator, fractional calculus

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DOI: 10.12732/ijpam.v93i3.3 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 93
Issue: 3
Pages: 325 - 337

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).