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A Cotangent Fractional Derivative with the Application

by Lakhlifa Sadek

Fractal Fract. 2023, 7(6), 444; https://doi.org/10.3390/fractalfract7060444 - 30 May 2023

Cited by 34 | Viewed by 2069

In this work, we present a new type of fractional derivatives (FD) involving exponential cotangent function in their kernels called Riemann–Liouville

$D^{σ, γ}$ and Caputo cotangent fractional derivatives

$^{C} D^{σ, γ}$ , respectively, and their corresponding integral [...] Read more.

In this work, we present a new type of fractional derivatives (FD) involving exponential cotangent function in their kernels called Riemann–Liouville

$D^{σ, γ}$ and Caputo cotangent fractional derivatives

$^{C} D^{σ, γ}$ , respectively, and their corresponding integral

$I^{σ, γ}$ . 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

$D^{σ, γ}$ ,

$^{C} D^{σ, γ}$ and

$I^{σ, γ}$ . 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. Full article

(This article belongs to the Special Issue Fractional Derivatives and Their Applications to Fractional Diffusion Problems)

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