Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843 - 7265 (print)
Volume 2 (2007), 145 - 156


Rabha W. Ibrahim and Shaher Momani

Abstract. In this paper we consider the integral equation of fractional order in sense of Riemann-Liouville operator

um(t) = a(t) Iα [b(t)u(t)]+f(t)
with m ≥ 1, t ∈ [0, T], T < ∞ and 0< α <1. We discuss the existence, uniqueness, maximal, minimal and the upper and lower bounds of the solutions. Also we illustrate our results with examples.

2000 Mathematics Subject Classification: 34G10; 26A33; 34A12; 42B05.
Keywords: Riemann-Liouville operators; Upper and lower bound of solution; Volterra integral equation.

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Rabha W. Ibrahim Shaher Momani
P.O. Box 14526, Sanaa, Department of Mathematics, Mutah University,
Yemen. P.O. Box 7, Al-Karak, Jordan.
e-mail: e-mail: