×

On the existence of extremal solutions of fractional integro-differential equations. (English) Zbl 0967.45005

The authors investigate the existence of extremal (maximal and minimal) solutions of the fractional integro-differential equations of the type: \[ x^{(\alpha)} (t)=f(t,x)+ \int^t_{t_0} K\bigl(t,s,x (s)\bigr)ds, \quad \alpha\in \mathbb{R},\;0<\alpha\leq 1. \] The comparison principle and Ascoli lemma have been used in establishing the main results. Also, a result that involves estimating a function satisfying a fractional integro-differential inequality by the extremal solution of the corresponding equation, is obtained.

MSC:

45J05 Integro-ordinary differential equations
45G10 Other nonlinear integral equations
26A33 Fractional derivatives and integrals
PDFBibTeX XMLCite