LYAPUNOV-TYPE INEQUALITIES FOR FRACTIONAL BOUNDARY VALUE PROBLEMS INVOLVING TWO GENERALIZED FRACTIONAL DERIVATIVES WITH RESPECT TO ANOTHER FUNCTION

Wei Zhang; Yue Sun; Jinbo Ni

doi:10.11948/20260053

2027 Volume 17 Issue 2

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Wei Zhang, Yue Sun, Jinbo Ni. LYAPUNOV-TYPE INEQUALITIES FOR FRACTIONAL BOUNDARY VALUE PROBLEMS INVOLVING TWO GENERALIZED FRACTIONAL DERIVATIVES WITH RESPECT TO ANOTHER FUNCTION[J]. Journal of Applied Analysis & Computation, 2027, 17(2): 632-651. doi: 10.11948/20260053

Citation:

Wei Zhang, Yue Sun, Jinbo Ni. LYAPUNOV-TYPE INEQUALITIES FOR FRACTIONAL BOUNDARY VALUE PROBLEMS INVOLVING TWO GENERALIZED FRACTIONAL DERIVATIVES WITH RESPECT TO ANOTHER FUNCTION[J]. Journal of Applied Analysis & Computation, 2027, 17(2): 632-651. doi: 10.11948/20260053

LYAPUNOV-TYPE INEQUALITIES FOR FRACTIONAL BOUNDARY VALUE PROBLEMS INVOLVING TWO GENERALIZED FRACTIONAL DERIVATIVES WITH RESPECT TO ANOTHER FUNCTION

1.
School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan, Anhui 232001, China

Author Bio: Email: sunyue_aust@163.com(Y. Sun); Email: nijinbo2005@126.com(J. Ni)
Corresponding author: Email: zhangwei_azyw@163.com(W. Zhang)
Fund Project: The authors were supported by the Key Project of Graduate Education and Teaching Reform of Anhui Province (2024jyjxggyjY180) and the Anhui Provincial Natural Science Foundation (2208085QA05)

Abstract

Abstract

This paper is devoted to the study of Dirichlet boundary value problems for fractional differential equations involving two types of fractional derivatives defined with respect to another function, introduced by Nieto et al. [22]. By constructing the corresponding generalized Green's functions and analyzing their structural properties, we derive necessary conditions for the existence of nontrivial solutions in the form of generalized Lyapunov-type inequalities. The results extend the classical Lyapunov inequality and contribute to the qualitative analysis of boundary value problems governed by generalized fractional derivatives.
- Generalized fractional derivatives /
- fractional differential equations /
- Dirichlet boundary conditions /
- Lyapunov-type inequalities
MSC: 34A08, 26A33, 34B05, 34B27

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References

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