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Nonlinear Degenerate Fractional Evolution Equations with Nonlocal Conditions

Derdar N., Debbouche A.

Fundamenta Informaticae

2017

Vol. 151, nr 1/4

473--485

We investigate the unique solvability of a class of nonlinear nonlocal differential equations associated with degenerate linear operator at the fractional Caputo derivative. For the main results, we use the theory of fractional calculus and (L, p)-boundedness technique that based on the analysis of both strongly (L, p)-sectorial operators and strongly (L, p)-radial operators. The obtained results are applicable to degenerate fractional Cauchy and Showalter–Sidorov problems in Banach spaces. Finally, we give an application described by time-fractional order Oskolkov system.