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The Cotangent Derivative with Respect to Another Function: Theory, Methods and Applications

Year: 2025

Type: article

Abstract: This paper introduces a generalization of the Riemann–Liouville and Caputo cotangent derivatives and their corresponding integrals, known as the Riemann–Liouville and Caputo cotangent derivatives with respect to another function (RAF). These fractional derivatives possess the advantageous property of forming a semigroup. The paper also presents a collection of theorems and lemmas, providing solutions to linear cotangent differential equations using the generalized Laplace transform. Moreover, we present the numerical approach, the application for solving the Caputo cotangent fractional Cauchy problem, and two examples for testing this approach.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract9110690

Authors: Lakhlifa Sadek, Ali Algefary

Institutions: Abdelmalek Essaâdi University, Saveetha University, Qassim University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,258

OpenAlex ID: W4415649223

FWCI: 7.444

Cites: 19

Cited by: 10

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