ON CONTROLLABILITY, STABILITY AND SOLVABILITY OF HILFER FRACTIONAL <i>q</i>-DYNAMICAL DELAY EQUATIONS ON TIME SCALES

Jufang Wang; Zinuo Jia; Changlong Yu

doi:10.11948/20250395

2027 Volume 17 Issue 1

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Jufang Wang, Zinuo Jia, Changlong Yu. ON CONTROLLABILITY, STABILITY AND SOLVABILITY OF HILFER FRACTIONAL q-DYNAMICAL DELAY EQUATIONS ON TIME SCALES[J]. Journal of Applied Analysis & Computation, 2027, 17(1): 389-412. doi: 10.11948/20250395

Citation:

Jufang Wang, Zinuo Jia, Changlong Yu. ON CONTROLLABILITY, STABILITY AND SOLVABILITY OF HILFER FRACTIONAL q-DYNAMICAL DELAY EQUATIONS ON TIME SCALES[J]. Journal of Applied Analysis & Computation, 2027, 17(1): 389-412. doi: 10.11948/20250395

ON CONTROLLABILITY, STABILITY AND SOLVABILITY OF HILFER FRACTIONAL q-DYNAMICAL DELAY EQUATIONS ON TIME SCALES

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

Author Bio: Email: wangjufang1981@126.com(J. Wang); Email: jiazinuo0621@126.com(Z. Jia)
Corresponding author: Email: changlongyu@126.com(C. Yu)

Abstract

Abstract

This article investigates a class of Hilfer-type fractional q-difference equations with time delay on time scales. Using Krasnoselskii's fixed point theorem and Banach contraction mapping principle, we obtain the existence and uniqueness of solutions for this equation. Meanwhile, we discuss the Hyers-Ulam stability of the solution for the equation by constructing a suitable perturbed equation, and obtain sufficient conditions of the controllability for the equation through the utilization of a non-zero bounded linear operator and a function that characterizes the control action. A numerical example is presented to validate the main results.
- q-fractional dynamical equations /
- time scales /
- existence /
- Hyers-Ulam stability /
- controllability
MSC: 39A13, 26A33, 34A08, 34N05, 93B05

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References

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