On solutions of fractional differential equations for the mechanical oscillations by using the Laplace transform

Changdev P. Jadhav; Tanisha B. Dale; Vaijanath L. Chinchane; Asha B. Nale; Sabri T.M. Thabet; Imed Kedim; Miguel Vivas-Cortez

doi:10.3934/math.20241562

On solutions of fractional differential equations for the mechanical oscillations by using the Laplace transform

Changdev P. Jadhav, Tanisha B. Dale, Vaijanath L. Chinchane, Asha B. Nale, Sabri T.M. Thabet^*, Imed Kedim, Miguel Vivas-Cortez^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In this article, we employ the Laplace transform (LT) method to study fractional differential equations with the problem of displacement of motion of mass for free oscillations, damped oscillations, damped forced oscillations, and forced oscillations (without damping). These problems are solved by using the Caputo and Atangana-Baleanu (AB) fractional derivatives, which are useful fractional derivative operators consist of a non-singular kernel and are efficient in solving non-local problems. The mathematical modelling for the displacement of motion of mass is presented in fractional form. Moreover, some examples are solved.

Original language	English
Pages (from-to)	32629-32645
Number of pages	17
Journal	AIMS Mathematics
Volume	9
Issue number	11
DOIs	https://doi.org/10.3934/math.20241562
State	Published - 2024

Bibliographical note

Publisher Copyright:
© 2024 the Author(s).

Keywords

Laplace transform
fractional derivative
fractional differential equations
oscillations

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10.3934/math.20241562

Cite this

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title = "On solutions of fractional differential equations for the mechanical oscillations by using the Laplace transform",

abstract = "In this article, we employ the Laplace transform (LT) method to study fractional differential equations with the problem of displacement of motion of mass for free oscillations, damped oscillations, damped forced oscillations, and forced oscillations (without damping). These problems are solved by using the Caputo and Atangana-Baleanu (AB) fractional derivatives, which are useful fractional derivative operators consist of a non-singular kernel and are efficient in solving non-local problems. The mathematical modelling for the displacement of motion of mass is presented in fractional form. Moreover, some examples are solved.",

keywords = "Laplace transform, fractional derivative, fractional differential equations, oscillations",

author = "Jadhav, {Changdev P.} and Dale, {Tanisha B.} and Chinchane, {Vaijanath L.} and Nale, {Asha B.} and Thabet, {Sabri T.M.} and Imed Kedim and Miguel Vivas-Cortez",

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doi = "10.3934/math.20241562",

language = "English",

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AU - Jadhav, Changdev P.

AU - Dale, Tanisha B.

AU - Chinchane, Vaijanath L.

AU - Nale, Asha B.

AU - Thabet, Sabri T.M.

AU - Kedim, Imed

AU - Vivas-Cortez, Miguel

PY - 2024

Y1 - 2024

N2 - In this article, we employ the Laplace transform (LT) method to study fractional differential equations with the problem of displacement of motion of mass for free oscillations, damped oscillations, damped forced oscillations, and forced oscillations (without damping). These problems are solved by using the Caputo and Atangana-Baleanu (AB) fractional derivatives, which are useful fractional derivative operators consist of a non-singular kernel and are efficient in solving non-local problems. The mathematical modelling for the displacement of motion of mass is presented in fractional form. Moreover, some examples are solved.

AB - In this article, we employ the Laplace transform (LT) method to study fractional differential equations with the problem of displacement of motion of mass for free oscillations, damped oscillations, damped forced oscillations, and forced oscillations (without damping). These problems are solved by using the Caputo and Atangana-Baleanu (AB) fractional derivatives, which are useful fractional derivative operators consist of a non-singular kernel and are efficient in solving non-local problems. The mathematical modelling for the displacement of motion of mass is presented in fractional form. Moreover, some examples are solved.

KW - Laplace transform

KW - fractional derivative

KW - fractional differential equations

KW - oscillations

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DO - 10.3934/math.20241562

M3 - Article

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SN - 2473-6988

VL - 9

SP - 32629

EP - 32645

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 11

ER -

On solutions of fractional differential equations for the mechanical oscillations by using the Laplace transform

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Keywords

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