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Cauchy problem for non-autonomous fractional evolution equations

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Abstract

In this paper, we study the solvability of Cauchy problem for a class of non-autonomous fractional evolution equation with Caputo’s fractional derivative of order \(\alpha \in (1,2)\), which can be applied to model the time dependent coefficients fractional differential systems. We first introduce an operator family and analyze its properties, by the iterative method, we construct a solution to an operator-valued Volterra equation, which is the most critical ingredient to prove solvability of the problem. Finally, based on the solution operators we establish the existence and uniqueness of classical solutions.

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Acknowledgements

The work was supported by National Natural Science Foundation of China (12071396, 12101142)

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Authors and Affiliations

  1. College of Mathematics and Information Science, Guangxi University, Nanning, 530004, China

    Jia Wei He

  2. Faculty of Mathematics and Computational Science, Xiangtan University, Hunan, 411105, China

    Yong Zhou

  3. School of Computer Science and Engineering, Macau University of Science and Technology, Macau, 999078, China

    Yong Zhou

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  1. Jia Wei He
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  2. Yong Zhou
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Correspondence to Yong Zhou.

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He, J.W., Zhou, Y. Cauchy problem for non-autonomous fractional evolution equations. Fract Calc Appl Anal 25, 2241–2274 (2022). https://doi.org/10.1007/s13540-022-00094-4

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