Physical Applications of the Bicomplex Fractional Laplace Transform: A Perception

Abstract The field of quaternions is an extension of the field of complex numbers. Quaternions do not satisfy commutativity. In the process of overcoming this drawback of non-commutativity, the system of bicomplex numbers, which is also a four-dimensional algebra that preserves commutativity, came into existence. Fractional calculus unifies and generalizes integer-order differentiation and integration. Theoretical knowledge of any concept is helpful in knowing the techniques and reasoning. But it is only the application that gives us insight into it. In this article, we have applied the bicomplex fractional Laplace transform to the differential equations that arise in electric circuits, nuclear physics, population growth, and heat equations. We have established relationships between beta and gamma functions, bicomplex fractional Laplace transforms, and Bessel’s functions. We have also used the relationship between beta and gamma functions to solve the differential equation governing the blood alcohol level.