Ibrahim, Rabha W.; Momani, Shaher Upper and lower bounds of solutions for fractional integral equations. (English) Zbl 1155.34301 Surv. Math. Appl. 2, 145-156 (2007). Summary: We consider the integral equation of fractional order in sense of Riemann-Liouville operator\[ u^m(t)= a(t)I^\alpha[b(t)u(t)]+f(t), \]with \(m\geq 1\), \(t\in [0,T]\), \(T<\infty\) and \(0<\alpha<1\). We discuss existence, uniqueness, maximal, minimal and the upper and lower bounds of the solutions. Also we illustrate our results with examples. Cited in 5 Documents MSC: 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations 26A33 Fractional derivatives and integrals 45G10 Other nonlinear integral equations Keywords:Riemann-Liouville operators; upper and lower bound of solution; Volterra integral equation PDFBibTeX XMLCite \textit{R. W. Ibrahim} and \textit{S. Momani}, Surv. Math. Appl. 2, 145--156 (2007; Zbl 1155.34301) Full Text: EuDML Link