Fractional Integral Inequalities and Their Applications to Degenerate Differential Equations with the Caputo Fractional Derivative

Abstract

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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Correspondence to A. N. Artyushin.

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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

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Keywords

  • fractional derivative
  • degenerate equation
  • integral inequality