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Theory of fractional differential inequalities and applications. (English) Zbl 1159.34006

The authors develop a theory of fractional differential inequalities involving Riemann-Liouville differential operators of fractional order. They use it to establish the existence of extremal solutions and of global solutions. Necessary conditions are discussed and the comparison principle is proved which will be useful for further study of qualitative behavior of solutions.

MSC:

34A40 Differential inequalities involving functions of a single real variable
26A33 Fractional derivatives and integrals
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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