Mathematics and Statistics Vol. 8(4), pp. 443 - 450
DOI: 10.13189/ms.2020.080411
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Triple Laplace Transform in Bicomplex Space with Application

Mahesh Puri Goswami ^1,*, Naveen Jha ^2
1 Department of Mathematics & Statistics, Mohanlal Sukhadia University, Udaipur-313001, India
² Department of Mathematics, Government Engineering College, Bharatpur-321303, India

ABSTRACT

In this article, we investigate bicomplex triple Laplace transform in the framework of bicomplexified frequency domain with Region of Convergence (ROC), which is generalization of complex triple Laplace transform. Bicomplex numbers are pairs of complex numbers with commutative ring with unity and zero-divisors, which describe physical interpretation in four dimensional spaces and provide large class of frequency domain. Also, we derive some basic properties and inversion theorem of triple Laplace transform in bicomplex space. In this technique, we use idempotent representation methodology of bicomplex numbers, which play vital role in proving our results. Consequently, the obtained results can be highly applicable in the fields of Quantum Mechanics, Signal Processing, Electric Circuit Theory, Control Engineering, and solving differential equations. Application of bicomplex triple Laplace transform has been discussed in finding the solution of third-order partial differential equation of bicomplex-valued function.

KEYWORDS
Bicomplex Functions, Triple Laplace Transform and Bicomplex Laplace Transform

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Mahesh Puri Goswami , Naveen Jha , "Triple Laplace Transform in Bicomplex Space with Application," Mathematics and Statistics, Vol. 8, No. 4, pp. 443 - 450, 2020. DOI: 10.13189/ms.2020.080411.

(b). APA Format:
Mahesh Puri Goswami , Naveen Jha (2020). Triple Laplace Transform in Bicomplex Space with Application. Mathematics and Statistics, 8(4), 443 - 450. DOI: 10.13189/ms.2020.080411.