SOLVABILITY OF HILFER FRACTIONAL DIFFERENTIAL EQUATIONS WITH INTEGRAL BOUNDARY CONDITIONS AT RESONANCE IN $ \mathbb{R}^M $

Huanmin Si; Weihua Jiang; Gongyu Li

doi:10.11948/20230410

2025 Volume 15 Issue 1

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Huanmin Si, Weihua Jiang, Gongyu Li. SOLVABILITY OF HILFER FRACTIONAL DIFFERENTIAL EQUATIONS WITH INTEGRAL BOUNDARY CONDITIONS AT RESONANCE IN $ \mathbb{R}^M $[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 39-55. doi: 10.11948/20230410

Citation:

Huanmin Si, Weihua Jiang, Gongyu Li. SOLVABILITY OF HILFER FRACTIONAL DIFFERENTIAL EQUATIONS WITH INTEGRAL BOUNDARY CONDITIONS AT RESONANCE IN $ \mathbb{R}^M $[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 39-55. doi: 10.11948/20230410

SOLVABILITY OF HILFER FRACTIONAL DIFFERENTIAL EQUATIONS WITH INTEGRAL BOUNDARY CONDITIONS AT RESONANCE IN $ \mathbb{R}^M $

1.
College of Sciences, Hebei University of Science and Technology, Shijiazhuang 050018, China

Author Bio: Email: sihuanmin97@163.com(H. Si); Email: 958454522@qq.com(G. Li)
Corresponding author: Email: jianghua64@163.com(W. Jiang)

Abstract

Abstract

In this paper, the solvability of a class of nonlinear Hilfer fractional differential equations boundary value problems is considered at resonance in $ \mathbb{R}^m $. The interesting point is that Hilfer is a more general differential operator that contains both the Riemann-Liouville and the Caputo derivative, and the dimension of the kernel of the fractional differential operator with Rimman-stieltjes integral boundary condition can take any value in $ \{1, 2, \cdots, m\} $. By applying Mawhin's coincidence degree theory, the existence result of solutions is obtained.
- Hilfer fractional differential equation /
- Mawhin's coincidence degree theory /
- resonance /
- Rimman-stieltjes integral
MSC: 34A08, 34B15

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References

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