EXISTENCE AND HYERS-ULAM STABILITY FOR BOUNDARY VALUE PROBLEMS OF TWO-TERM FRACTIONAL DIFFERENTIAL EQUATIONS WITH $ \kappa $-CAPUTO DERIVATIVE

Xiaoping Xu; Ziang Shen; Shangzhi Liu; Qixiang Dong

doi:10.11948/20240526

2025 Volume 15 Issue 5

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Xiaoping Xu, Ziang Shen, Shangzhi Liu, Qixiang Dong. EXISTENCE AND HYERS-ULAM STABILITY FOR BOUNDARY VALUE PROBLEMS OF TWO-TERM FRACTIONAL DIFFERENTIAL EQUATIONS WITH $ \kappa $-CAPUTO DERIVATIVE[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 2786-2804. doi: 10.11948/20240526

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Xiaoping Xu, Ziang Shen, Shangzhi Liu, Qixiang Dong. EXISTENCE AND HYERS-ULAM STABILITY FOR BOUNDARY VALUE PROBLEMS OF TWO-TERM FRACTIONAL DIFFERENTIAL EQUATIONS WITH $ \kappa $-CAPUTO DERIVATIVE[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 2786-2804. doi: 10.11948/20240526

EXISTENCE AND HYERS-ULAM STABILITY FOR BOUNDARY VALUE PROBLEMS OF TWO-TERM FRACTIONAL DIFFERENTIAL EQUATIONS WITH $ \kappa $-CAPUTO DERIVATIVE

1.
School of Basic Sciences, Nantong Vocational University, Nantong 226007, China
2.
School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China

Author Bio: Email: xuxp@mail.ntvu.edu.cn(X. Xu); Email: 200803124@stu.yzu.edu.cn(Z. Shen); Email: 191503409@stu.yzu.edu.cn(S. Liu)
Corresponding author: Email: qxdong@yzu.edu.cn(Q. Dong)
Fund Project: The authors were supported by National Natural Science Foundation of China (12271469 and 12371140) and Jiangsu Students' Innovation and Entrepreneurship Training Program (202211117093Y)

Abstract

Abstract

This paper is concerned with a class of nonlinear fractional differential equations with two-term $ \kappa $-Caputo fractional derivatives. The existence and uniqueness results are obtained for boundary value problems by using the Banach fixed point theorem and Leray-Schauder nonlinear alternative. The Hyers-Ulam stability is also considered. Some examples are discussed to illustrate the obtained results.
- Fractional differential equations /
- boundary value problem /
- mild solution /
- fixed point theorem /
- stability
MSC: 34A08, 34D20, 47H10

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