A note on the fractional calculus in Banach spaces-Reference-Cited by-同舟云学术

A note on the fractional calculus in Banach spaces

Published:2005-05-01 Issue:2 Volume:42 Page:115-130
ISSN:0081-6906
Container-title:Studia Scientiarum Mathematicarum Hungarica
language:
Short-container-title:

Author:

Salem Hussein A. H.¹,El-Sayed A. M. A.²,Moustafa O. L.³

Affiliation:

1. 1 Department of Mathematics, Faculty of Sciences, Alexandria University Alexandria, Egypt

2. 2 Department of Mathematics, Faculty of Sciences, Alexandria University Alexandria, Egypt

3. 3 Department of Mathematics, Faculty of Sciences, Alexandria University Alexandria, Egypt

Abstract

O'Regan fixed point theorem is used to establish an existence result for the fractional order integral equation x(t) = g(t)+ ?Ia f(.,x(.))(t), t?[0,1], a ? 0, where the vector-valued function f is nonlinear weakly-weakly continuous. Moreover, existence of weak solutions to the Cauchy problem dx/dt = f(t, x (t)), t ? [0,1], x(0) = x0, is obtained as a corollary.

Publisher

Akademiai Kiado Zrt.

Subject

General Mathematics

Link

https://www.akademiai.com/doi/pdf/10.1556/sscmath.42.2005.2.1

Reference24 articles.

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2. Nonlinear functional differential equations of arbitrary orders. Nonlinear Analysis: Theory, Methods and applications 33;A. El-Sayed;Nonlinear Anal.,1998

3. Set-valued integral equations of arbitrary (fractional) order;A. El-Sayed;Appl.Math. Comput.,2001

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