On a differential equation with Caputo-Fabrizio fractional derivative of order $1<\beta\leq 2$ and application to mass-spring-damper system

By N. Al-Salti, Erkinjon Tulkinovich Karimov, Kishin B. Sadarangani. 2016

63 citations recorded by the source corpus.

In this work, we investigate a linear differential equation involving Caputo-Fabrizio fractional derivative of order $1<\beta\leq 2$. Under some assumptions the considered equation is reduced to an integer order differential equation and solutions for different cases are obtained in explicit forms. We also prove a uniqueness of a solution of an initial value problem with a nonlinear differential equation containing the Caputo-Fabrizio derivative. Application of our result to the mass-spring-damper motion is also presented.

Subfields: Applied Mathematics, Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1a700cfa8b629a189de0412d03b4f0aa32979f2f

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In Applied Mathematics

In Modeling and Simulation

In Statistical and Nonlinear Physics

Citations in the corpus

On some new properties of fractional derivatives with Mittag-Leffler kernel (2017, methodology): “The Caputo–Fabrizio definition has already found applications in areas such as diffusion modelling [20] and mass-spring-damper systems [7].”