On the Application of Complex Delta Function Leading to New Fractional Calculus Formulae Involving the Generalized Hypergeometric Function and Kinetic Equation

Abstract

The sun is a vital component of our natural environment, and kinetic equations are important mathematical models that show how quickly a star’s chemical composition changes. Taking inspiration from these facts, we develop and solve a novel fractional kinetic equation by calculating the Laplace transform of hypergeometric functions in the complex coefficient parameter. This was a challenging task because the function cannot be integrated concerning the coefficient parameters using classical methods due to the infinite number of singular points of the gamma function involved in it. We achieved it using the distributional representation of the generalized hypergeometric function. Moreover, on the one hand, the role of the delta function is vital to represent the electromotive forces, and on the other, the solution of differential equations of engineering and mathematical physics led to a class of hypergeometric functions. This article is the confluence of both. Therefore, innovative characteristics concerning the Fox-Wright and several related important functions are applied for the simplification of the obtained outcomes. A popular class of fractional transforms involving generalized hypergeometric functions are evaluated using the delta function, and as a distribution, numerous additional features of this function are described.