article · Fractal and Fractional
New mathematical operators known as Riemann-Liouville and Caputo cotangent fractional derivatives, alongside their corresponding fractional integral, have been introduced using exponential cotangent functions in their kernels. These formulations satisfy a desirable semi-group property and generalise standard fractional calculus definitions, recovering classic Riemann-Liouville and Caputo forms under specific parameter conditions. The theoretical framework includes foundational theorems, lemmas, and analytical solutions for linear cotangent fractional differential equations determined via Laplace transforms. To demonstrate practical relevance, the formulation is applied to the classic Susceptible-Infectious-Recovered epidemiological model. This mathematical development offers an extended framework intended to assist researchers working on fractional differential equations to model complex dynamic processes.
Fractional calculus provides powerful tools to model complex biological and physical phenomena that standard calculus cannot fully capture. By establishing new derivative operators that maintain beneficial algebraic properties and generalise existing approaches, this research enhances mathematical modelling capabilities for non-linear dynamic systems, such as infectious disease transmission tracking.
This work represents early-stage fundamental mathematical research. Although the new derivative is demonstrated on an epidemiological SIR model, which is typically relevant to disease modelling specialists and public health analysts, the research remains theoretical. The abstract does not indicate a direct commercialisation pathway or commercial product.
AI-generated from the published abstract. Always read the original work before citing.
In this work, we present a new type of fractional derivatives (FD) involving exponential cotangent function in their kernels called Riemann–Liouville Dσ,γ and Caputo cotangent fractional derivatives CDσ,γ, respectively, and their corresponding integral Iσ,γ. The advantage of the new fractional derivatives is that they achieve a semi-group property, and we have special cases; if γ=1 we obtain the Riemann–Liouville FD (RL-FD), Caputo FD (C-FD), and Riemann–Liouville fractional integral (RL-FI). We give some theorems and lemmas, and we give solutions to linear cotangent fractional differential equations using the Laplace transform of the Dσ,γ, CDσ,γ and Iσ,γ. Finally, we give the application of this new type on the SIR model. This new type of fractional calculus can help other researchers who still work on the actual subject.
This page summarises published work. The authoritative version sits with the publisher.
DOI: 10.3390/fractalfract7060444
Is something wrong with this record? Report it or request removal.
Discussion
Have you built on this work, tried to replicate it, or seen it applied in practice? Share what you know. Verified researchers and MARATTO™ domain experts can open a discussion, and any member can reply. Contributions are reviewed before they appear.
No discussion yet. Open the first thread.
New to MARATTO™? Create a free account.
