EXISTENCE FOR NONLINEAR FRACTIONAL EVOLUTIONARY EQUATIONS INVOLVING $\psi$-CAPUTO FRACTIONAL DERIVATIVE

Biao Zeng; Shuhua Wang

doi:10.11948/20230243

2024 Volume 14 Issue 3

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Biao Zeng, Shuhua Wang. EXISTENCE FOR NONLINEAR FRACTIONAL EVOLUTIONARY EQUATIONS INVOLVING $\psi$-CAPUTO FRACTIONAL DERIVATIVE[J]. Journal of Applied Analysis & Computation, 2024, 14(3): 1414-1433. doi: 10.11948/20230243

Citation:

Biao Zeng, Shuhua Wang. EXISTENCE FOR NONLINEAR FRACTIONAL EVOLUTIONARY EQUATIONS INVOLVING $\psi$-CAPUTO FRACTIONAL DERIVATIVE[J]. Journal of Applied Analysis & Computation, 2024, 14(3): 1414-1433. doi: 10.11948/20230243

EXISTENCE FOR NONLINEAR FRACTIONAL EVOLUTIONARY EQUATIONS INVOLVING $\psi$-CAPUTO FRACTIONAL DERIVATIVE

Biao Zeng^1, ,,
Shuhua Wang^2,

1.
School of Mathematics and Physics, Center for Applied Mathematics of Guangxi, Guangxi Minzu University, Nanning 530006, Guangxi Province, China
2.
School of Mathematics and Physics, Center for Applied Mathematics of Guangxi, Guangxi Minzu University, Nanning 530006, Guangxi Province, China

Author Bio: Email: shuhua_wang0721@163.com(S. Wang)
Corresponding author: Email: biao_zeng@163.com(B. Zeng)
Fund Project: The authors were supported by National Natural Science Foundation of China (12201137), Special Fund for Science and Technological Bases and Talents of Guangxi (GUIKE AD21220103) and Start-up Project of Scientific Research on Introducing talents at school level in Guangxi Minzu University (2019KJQD04)

Abstract

Abstract

The aim of this paper to deal with a new class of fractional evolutionary equations involving $\psi$-Caputo fractional derivative and nonlinear weakly continuous operators. Exploiting the Rothe method and using a surjectivity result for weakly continuous operators, the solvability for the problem is established. The result is applied to a quasistatic frictional contact problem.
- Fractional evolutionary equation /
- $\psi$-Caputo fractional derivative /
- weakly continuous operator /
- quasistatic frictional contact problem
MSC: 35K86, 47J22, 65M12, 76D05

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References

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