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Upper and lower bounds of solutions for fractional integral equations. (English) Zbl 1155.34301

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.

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
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