# Applications of Fractional-Laplace Transformation in the Field of Electrical Engineering

## Authors

• Ali Moazzam Department of mathematics and statistics, university of agriculture Faisalabad Pakistan
• Zainab Ijaz Department of mathematics and Statistics University of Agriculture Faisalabad. Faisalabad, Pakistan https://orcid.org/0009-0006-3393-3132
• Muhammad Hussain Department of Physics University of Agriculture Faisalabad. Faisalabad, Pakistan https://orcid.org/0009-0001-9526-3270
• Nimra Maqbool Department of Physics University of Agriculture Faisalabad. Faisalabad, Pakistan https://orcid.org/0009-0007-5131-0024
• Emad A. Kuffi Department of mathematics School of Engineering, University of Al-Qadisiyah. Iraq.

## Keywords:

Fractional-Laplace transformation;, Circuit equations, Heat conduction differential model, linear differential equations, time derivative rule

## Abstract

This study examines the various ways that fractional Laplace transform can be used to solve three different kinds of mathematical equations: the equation of analysis of electric circuits, simultaneous differential equations, and the heat conduction equation. This article how to use the fractional Laplace transform to calculate heat flow in semi-infinite solids in the context of heat conduction. The answers that are developed offer important information about how temperatures vary across time and space. The essay also examines how to analyse electrical circuits using the Fractional Laplace transform. This method allows researchers to measure significant electrical parameters including charge and current, which improves their comprehension of circuit dynamics. Practical examples are included throughout the essay to show how useful the Fractional Laplace transform is in various fields. As a result of the answers found using this methodology, researchers and engineers working in the fields of heat conduction, system dynamics, and circuit analysis can gain important new knowledge. In conclusion, this study explains the applicability and effectiveness of the fractional Laplace transform in resolving a variety of mathematical equations. It is a vital tool for researchers because it may be used in a wide range of scientific and engineering areas.

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## References

Q. Gong, C. Liu, Y. Xu, C. Ma, J. Zhou, R. Jiang, and C. Zhou, “Nonlinear vibration control with nanocapacitive sensor for electrostatically actuated nanobeam” J. Low Freq., Vol. 37, Issue 2, 2018, Pp. 235-252.

M.S. El-Azab, and M.A. El-Gamel, “Numerical algorithm for the solution of telegraph equations” Appl. Math. Comput., Vol. 190, Issue 1, 2007, Pp. 757-764.

S. Pandit, M. Kumar, and S. Tiwari, “Numerical simulation of second-order hyperbolic telegraph type equations with variable coefficients”,

Comput. Phys. Commun, Vol. 187, 2015, Pp. 83-90.

D.J. Evans, and H. Bulut, “The numerical solution of the telegraph equation by the alternating group explicit (AGE) method”, Int. J. Comput. Math., Vol. 80, Issue 10, 2003, Pp. 1289-1297.

H.F. Ding, Y.X. Zhang, J.X. Cao, and J.H. Tian, “A class of difference scheme for solving telegraph equation by new non-polynomial spline methods”,

Appl. Math. Comput., Vol. 218, Issue 9, 2013, Pp. 46714683.

D.J. Evans, and K.R. Raslan, “The Adomian decomposition method for solving delay differential equation” Int. J. Comput. Math.. Vol. 82, Issue 1, 2005, Pp. 49-54.

M.A. Mohamed, M.S. Torky, “Numerical solution of nonlinear system of partial differential equations by the

Kamal decomposition method and the Pade approximation”, Am. J. Comput. Math., Vol. 3, Issue 3, 2013, Pp. 175-183.

J.B. Yindoula, P. Youssouf, G. Bissanga, and F. Bassono,

“Application of the Adomian decomposition method and Laplace transform method to solving the convection diffusion-dissipation equation” Int. J. Appl. Math., Vol. 3, Issue 1, 2014, Pp. 30-37.

A.A. Hamoud, and K.P. Ghadle, “The combined modified Laplace with Adomian decomposition method for solving

the nonlinear Volterra-Fredholm integro differential equations” J-KSIAM, Vol. 21, Issue 1, 2017, Pp. 17-28.

M. Fariha, Z.I. Muhammad, A. Moazzam, A. Usman, and

U.N Muhammad, “Subtituition Method using the Laplace transformation for solving partial differential equations involving more than two independent variables”, BOMSR, Vol. 9, Issue 3, 2021, Pp. 104-116.

I.K. Muhammad, S. Khurrem, M.U.R. Muhammad,

Maria, and A. Moazzam, “Influence of bioconvection and activation energy on maxwell flow of nano-fluid in the

existence of motile microorganisms over a cylinder”, Int.

j. multidiscip. res. dev., Vol. 2, Issue 5, 2021, Pp. 135-144.

A. Ammara, G. Madiha G, A. Amina, and A. Moazzam, “Laplace transforms techniques on equation of advectiondiffussion in one-dimensional with semi-infinite medium to find the analytical solution”, BOMSAR, Vol. 9, Issue 3, 2021, Pp. 86-96.

K. Muhammad, S. Khurrem, A. Moazzam, A. Ammara.

and B. Mariyam, “New transformation ‘AMKtransformation’ to solve ordinary linear differential equation of moment Pareto distribution”, Int. j. multidiscip. res. dev., Vol. 2, Issue 5, 2021, Pp. 125-134.

A. Moazzam, M. Kashif M, U. Amjed, and M.I. Khawar, “Devolpment of a new transformation to solve a new type of ordinary linear differential equation”, BOMSAR, Vol. 9, Issue 3, 2021, Pp. 56-60.

W. Muhammad; S. Khurrem, A. Moazzam, and B. Alizay, “Applications of Kamal transformation in temperature problems”, S. J. Eng. Tech., Vol. 10, Issue 2, 2022, Pp. 5-

A. Eman, Mansour, A.K. Emad, A. Sadiq, and Mehdi, “On the SEE transform and system of ordinary differential equations”, Period. Eng. Nat. Sci., Vol. 9, Issue 3, 2021, Pp. 277-281.

A. Moazzam, and Z.I. Muhammad, “Al-Zughair transformations on linear differential equations of Moment Pareto distribution”, Proc. 19th ICOSS, Vol. 36, 2022, Pp. 199-206.

A. Moazzam, and Z.I. Muhammad, “A new integral transform "Ali And Zafar" transformation and It's application in nuclear physics”, Proc. 19th ICOSS, Vol. 36, 2022, Pp. 177-182.

A. Daci, “Mathematical Models for Population Projection in Albania”, J. multidiscip. eng. sci. technol., Vol. 3, Issue 8, 2016, pp. 5486-5489.

A. Daci, and S. Tola, “Laplace transform applications in population growth”, Int. J. Eng. Technol., vol. 8 Issue-2, 2019, Pp. 478-484.

L.S. Sawant, “Applications of Laplace Transform in Engineering Fields” Int. Res. J. Eng. Technol., Vol. 05 Issue 5, 2018, Pp. 3100-3105.

N.A. Patil, N. Vijaya, and N. Patil, “Application of Laplace Transform”, Glob. J. sci. front. res. Math. & dec. sci., Vol. 12, Issue 12, 2012, Pp. 34-40.

A.K.T.R. Kumar, and G. Sahu, “Applications of Laplace transform on solutions of Fractional Differential Equations”, Int. j. comput. sci., Vol. 9, Issue 5, 2020, Pp. 478-484.

J.K. Rani, and S. Devi, “Laplace transform and its applications in engineering fields”, IJCOT, Vol. 5, Issue 2, 2015, Pp. 77-80.

M.C. Anumaka, “Analysis And Applications Of Laplace /Fourier Transformations In Electric Circuit” Int. J. Appl., Vol. 12, Issue2, 2012, Pp. 333-339.

A. Ivic, “Some applications of Laplace transforms in analytic number theory” Novi. Sad. J. Math. Vol. 1, 2015, Pp. 31-44.

G.D. Medina, N.R. Ojeda, J.H. Pereira, and L.G. Romero,

“Fractional Laplace transform and fractional calculus” Math. Forum., Vol. 12, Issue 20, 2017, Pp. 991-1000.

X. Geng, H. Cheng and M. Liu, “Inverse source problem of heat conduction equation with time-dependent diffusivity on a spherical symmetric domain”, Inverse Prob. Sci. & Eng., Vol. 29, Issue11, 2021, Pp. 1653-1668.

Vahedi, Vahid, and G. DiPeso. “Simultaneous potential and circuit solution for two-dimensional bounded plasma simulation codes”, J. Comp. Phy, Vol. 131, Issue 1, 1997, Pp. 149-163.

P. Borjesson, and C.E. Sundberg, "Simple approximations of the error function Q (x) for communications applications" IEEE Tran. Comm. Vol. 27, Issue, 3, 1979, Pp. 639-643.

2023-08-31

## How to Cite

Moazzam, A., Ijaz, Z., Hussain, M., Maqbool, N., & A. Kuffi, E. (2023). Applications of Fractional-Laplace Transformation in the Field of Electrical Engineering . Journal of Kufa for Mathematics and Computer, 10(2), 70–75. https://doi.org/10.31642/JoKMC/2018/100211

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