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Asymptotics and large time behaviors of fractional evolution equations with temporal ψ-Caputo derivative

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  • Li, Zhiqiang

Abstract

This paper devotes to developing the asymptotics and large time behaviors of fractional evolution equations, where the temporal derivative is the ψ-Caputo one of orders α∈(0,1) and α∈(1,2) and fractional Laplacian of order s∈(0,1) is used in the spatial direction. We first derive the solution of convolution form to the considered equation with α∈(0,1) in terms of integral transforms and then prove that it is a classical solution. Next, the asymptotic properties of the solution to this equation are established by Young’s inequality for convolution in the Lp(Rd) and Lp,∞(Rd) norms. In addition, the spatial derivative estimates and large time behavior of the solution are also provided. Finally, the corresponding results for α∈(1,2) are presented in a similar manner.

Suggested Citation

  • Li, Zhiqiang, 2022. "Asymptotics and large time behaviors of fractional evolution equations with temporal ψ-Caputo derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 210-231.
    • Handle: RePEc:eee:matcom:v:196:y:2022:i:c:p:210-231
    DOI: 10.1016/j.matcom.2022.01.023
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