Generalization of fractional Laplace transform for higher order and its application

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Ahmed Bouchenak
https://orcid.org/0000-0002-2898-0341

Abstract

In this paper, we first introduce the conformable fractional Laplace transform. Then, we give its generalization for higher-order. Finally, as an application, we solve a non-homogeneous conformable fractional differential equation with variable coefficients and a system of fractional differential equations.

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How to Cite
[1]
Bouchenak, A. 2021. Generalization of fractional Laplace transform for higher order and its application. Journal of Innovative Applied Mathematics and Computational Sciences. 1, 1 (Dec. 2021), 79–92. DOI:https://doi.org/10.58205/jiamcs.v1i1.2.
Section
Research Articles

References

T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math. 279(1) (2015), 57–66.

M. Abu Hammad and R. Khalil, Fractional Fourier Series with Applications, Amer. J. Comput. Appl. Math. 4(6) (2014), 187–191.

Z. Al-zhour, F. Alrawajeh, N. Al-mutairi and R. Alkhasawneh, New results on the conformable fractional Sumudu transforms: Theories and applications, International Journal of

Analysis and Applications. 17(6) (2019), 1019–1033.

D. R. Anderson, E. Camrud and D. J. Ulness, On the nature of the conformable derivative and its applications to physics, JJ. Fract. Calc. Appl. 10(2) (2019), 92–135.

A. Atangana and D. Baleanu, New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model, Therm. Sci. 20(2) (2016), 763–769.

M. Ayata and O. Ozkan, A new application of conformable Laplace decomposition method for fractional Newell-Whitehead-Segel equation, AIMS Math. 5(6) (2020), 7402–7412.

A. Bouchenak, R. Khalil, and M. AlHorani, Fractional Fourier Series with Separation of Variables Technique and its Application on Fractional Differential Equations, Wseas Transactions on Mathematics. 20 (2021), 461-469. DOI: 10.37394/23206.2021.20.48

A. Bushnaque, M. AlHorani and R. Khalil, Tensor product technique and atomic solution of fractional Bate Man Burger equation, J. math. Comput. Sci. 11(1) (2021), 330–336.

M. Caputo and M. Fabrizio, A new definition of fractional derivative without singular kernel, Progr. Fract. Differ. Appl. 1(2) (2015), 1–13.

A. Gokdogan, E. Unal, and E. Celik, Existence and Uniqueness Theorems for Sequential Linear Conformable Fractional Differential Equations, Miskolc Math. Notes 17 (1) (2016), 267–279. DOI: 10.18514/MMN.2016.1635

R. Khalil, M. Al Horani and D. Anderson, Undetermined coefficients for local fractional differential equations, J. Math. Computer Sci. 16 (2016), 140–146.

R. Khalil, M. Al Horani, A. Yousef and M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math. 264(2014), 65–70.

N. A. Khan, O. A. Razzaq, and M. Ayaz, Some properties and applications of conformable fractional Laplace transform (CFLT), J. Fract. Calc. Appl. 9(1) (2018), 72–81.

A. Kilbas, Hadamard-type fractional calculus. J. Korean Math. Soc. 38(6) (2001), 1191–1204.

K. S. Miller, An introduction to fractional calculus and fractional differential equations, J. Wiley Sons, New York, 1993.

D. A. Murio, Stable numerical evaluation of Grünwaldâ˘A ¸SLetnikov fractional derivatives applied to a fractional IHCP, Inverse Prob. Sci. Eng. 17(2) (2009), 229–243.

K. Oldham, J. Spanier, The Fractional Calculus, Theory and Applications of Differentiation and Integration of Arbitrary Order, Academic Press, USA, 1974.

F. S. Silva, D. M. Moreira, M. A. Moret, Conformable Laplace Transform of Fractional Differential Equations. J. axioms, 7(3) (2018), 50. DOI: 10.20944/preprints201807.0025.v1

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