EXISTENCE AND MULTIPLICITY RESULTS FOR A CLASS OF DISCRETE FRACTIONAL PROBLEMS WITH SUMMATION BOUNDARY CONDITIONS

Shugui Kang; Huiqin Chen; Yaqiong Cui; Luping Li; Wenying Feng

doi:10.11948/20250176

2026 Volume 16 Issue 4

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Shugui Kang, Huiqin Chen, Yaqiong Cui, Luping Li, Wenying Feng. EXISTENCE AND MULTIPLICITY RESULTS FOR A CLASS OF DISCRETE FRACTIONAL PROBLEMS WITH SUMMATION BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2026, 16(4): 2019-2033. doi: 10.11948/20250176

Citation:

Shugui Kang, Huiqin Chen, Yaqiong Cui, Luping Li, Wenying Feng. EXISTENCE AND MULTIPLICITY RESULTS FOR A CLASS OF DISCRETE FRACTIONAL PROBLEMS WITH SUMMATION BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2026, 16(4): 2019-2033. doi: 10.11948/20250176

EXISTENCE AND MULTIPLICITY RESULTS FOR A CLASS OF DISCRETE FRACTIONAL PROBLEMS WITH SUMMATION BOUNDARY CONDITIONS

1.
The Institute of Applied Mathematics, Shanxi Datong University, Datong 037009, Shanxi, China
2.
Department of Computer Science, Department of Mathematics & Statistics, Trent University Durham GTA (Greater Toronto Area), Oshawa L1J 5Y1, ON, Canada

Author Bio: Email: dtdxchq@126.com(H. Chen); Email: cuiyaqiongdt@163.com(Y. Cui); Email: llp12309845876@163.com(L. Li)
Corresponding authors: Email: dtkangshugui@126.com(S. Kang); Email: wfeng@trentu.ca(W. Feng)

Abstract

Abstract

We study a discrete boundary value problem involving the Riemann-Liouville fractional operator. In particular, we introduce a discrete fractional summing boundary value problem that parallels the integral boundary value problem for fractional differential equations. By generalizing a commonly used fractional difference operator, we derive the corresponding Green's function and reformulate the problem as a fixed-point equation. The existence and multiplicity of positive solutions are established. Two illustrative examples are provided to demonstrate the applicability of the theoretical results, and numerical simulations are included for further validation.
- Fractional difference equation /
- fixed point theory /
- summing boundary condition /
- numerical simulation /
- positive solution
MSC: 39A12, 39A70, 34B10

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References

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