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Journal of Mathematics and Applications

Journal of Mathematics and Applications
6/40, DOI: 10.7862/rf.2017.6

Weak Solutions of Fractional Order Differential Equations via Volterra-Stieltjes Integral Operator

A.M.A. El-Sayed, W.G. El-Sayed, A.A.H. Abd El-Mowla

DOI: 10.7862/rf.2017.6

Abstract

The fractional derivative of the Riemann-Liouville and Caputo types played an important role in the development of the theory of fractional derivatives, integrals and for its applications in pure mathematics([18], [ 21]). In this paper, we study the existence of weak solutions for fractional differential equations of Riemann-Liouville and Caputo types. We depend on converting of mentioned equations to the form of functional integral equations of Voltera-Stieltjes type in reflexive Banach spaces.

Full text (pdf)

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About this Article

TITLE:
Weak Solutions of Fractional Order Differential Equations via Volterra-Stieltjes Integral Operator

AUTHORS:
A.M.A. El-Sayed (1)
W.G. El-Sayed (2)
A.A.H. Abd El-Mowla (3)

AUTHORS AFFILIATIONS:
(1) Faculty of Science, Alexandria University, Alexandria, Egypt
(2) Faculty of Science, Alexandria University, Alexandria, Egypt
(3) Faculty of Science, Omar Al-Mukhtar University, Derna, Libya

JOURNAL:
Journal of Mathematics and Applications
6/40

KEY WORDS AND PHRASES:
Weak solution; Mild solution; Weakly Riemann-Stieltjes integral; Function of bounded variation

FULL TEXT:
http://doi.prz.edu.pl/pl/pdf/jma/55

DOI:
10.7862/rf.2017.6

URL:
http://dx.doi.org/10.7862/rf.2017.6

RECEIVED:
2017-03-01

COPYRIGHT:
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