We provide some new integral inequalities with the Caputo fractional derivative and consider degenerate ODEs with the Caputo derivative and a fractional diffusion equation as application. Also, we prove the existence and uniqueness theorems of generalized solutions under certain conditions.
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Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 2, pp. 266–282.
The author was supported by the Russian Foundation for Basic Research (Grant 18-51-41009).
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Artyushin, A.N. Fractional Integral Inequalities and Their Applications to Degenerate Differential Equations with the Caputo Fractional Derivative. Sib Math J 61, 208–221 (2020). https://doi.org/10.1134/S0037446620020032
- fractional derivative
- degenerate equation
- integral inequality