φ-Hilfer分数阶共振边值问题解的存在性

Journal of Jilin University Science Edition ›› 2023, Vol. 61 ›› Issue (5): 1019-1028.

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Existence of Solutions of φ-Hilfer Fractional Order Boundary Value Problems at Resonance

SI Huanmin, JIANG Weihua

School of Sciences, Hebei University of Science and Technology, Shijiazhuang 050018, China

Received:2022-11-22 Online:2023-09-26 Published:2023-09-26

Abstract

Abstract: By using Mawhin’s coincidence degree theory, we study the existence of solutions for the φ-Hilfer fractional order Riemman-Stieltjes integral boundary value problem. The results show that the solutions of φ-Hilfer fractional differential equation exist under the Riemann-Stieltjes integral boundary value conditions in suitable Banach spaces.

Key words: φ-Hilfer fractional derivative, Mawhin’s coincidence degree theory, Fredholm operator, boundary value problem, resonance

CLC Number:

O175.8

SI Huanmin, JIANG Weihua. Existence of Solutions of φ-Hilfer Fractional Order Boundary Value Problems at Resonance[J].Journal of Jilin University Science Edition, 2023, 61(5): 1019-1028.

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Existence of Solutions of φ-Hilfer Fractional Order Boundary Value Problems at Resonance

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