A non-linear fractional neutral dynamic equations: existence and stability results on time scales

Kottakkaran Sooppy Nisar; C. Anusha; C. Ravichandran; Kottakkaran Sooppy Nisar; C. Anusha; C. Ravichandran

doi:10.3934/math.2024094

AIMS Mathematics

2024, Volume 9, Issue 1: 1911-1925. doi: 10.3934/math.2024094

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Research article

A non-linear fractional neutral dynamic equations: existence and stability results on time scales

1.
Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia
2.
Department of Mathematics, Kongunadu Arts and Science College, Coimbatore 641029, India

Received: 02 October 2023 Revised: 02 December 2023 Accepted: 11 December 2023 Published: 18 December 2023
MSC : 37C25, 26E70, 34K40, 34N05

The outcomes of a nonlinear fractional neutral dynamic equation with initial conditions on time scales are examined in this work using the Riemann-Liouville nabla ($ \nabla $) derivative. The existence, uniqueness, and stability results for the solution are examined by using standard fixed point techniques. For the result illustration, an example is given along with the graph using MATLAB.
- neutral differential equations,
- Riemann-Liouville (RL) $ \nabla $-derivative,
- time scales,
- fixed point
Citation: Kottakkaran Sooppy Nisar, C. Anusha, C. Ravichandran. A non-linear fractional neutral dynamic equations: existence and stability results on time scales[J]. AIMS Mathematics, 2024, 9(1): 1911-1925. doi: 10.3934/math.2024094

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Abstract

The outcomes of a nonlinear fractional neutral dynamic equation with initial conditions on time scales are examined in this work using the Riemann-Liouville nabla ($ \nabla $) derivative. The existence, uniqueness, and stability results for the solution are examined by using standard fixed point techniques. For the result illustration, an example is given along with the graph using MATLAB.

References

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