A Novel approach for vector Lyapunov functions and practical stability of Caputo fractional dynamic equations on time scale in terms of two measures

Document Type : Original Article

Authors

Michael Precious Ineh ¹

Vivian Ndfutu Nfor ²

Marshal Imeh Sampson ³

Jackson Efiong Ante ⁴

Jeremiah Ugeh Atsu ⁵

Okoi Okoi Itam ⁶

¹ Department of Mathematics and Computer Science, Ritman University, Ikot Ekpene, Akwa Ibom State, Nigeria.

² Higher Technical Teacher Training College Bambili, The University of Bamenda, Cameroon

³ Department of Mathematics, Akwa Ibom State University, Nigeria.

⁴ Department of Mathematics, Topfaith University, Mkpatak, Nigeria.

⁵ Department of Mathematics, University of Cross River State, Calabar, Nigeria

⁶ Department of Mathematics, University of Calabar, Nigeria.

10.22034/kjm.2025.487084.3362

Abstract

This paper presents a novel approach to analyzing the practical stability of Caputo fractional dynamic equations on time scales in terms of two measures ($m,m_0$), utilizing a new generalized derivative known as the Caputo fractional delta derivative and the Caputo fractional delta Dini derivative of order \(\alpha \in (0,1)\). This generalized concept not only provides a unified framework for analyzing dynamic systems across both continuous and discrete time domains, but it also includes and unifies several known concepts of stability in a single setup making it suitable for hybrid systems exhibiting both gradual and abrupt changes.The established two measures practical stability results are demonstrated through an illustrative example.

Keywords

Fractional calculus

Stability analysis

Dynamic systems

Subjects

• 34 Ordinary differential equations

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