Extorial Solutions for Fractional and Partial Difference Equations with Applications: A Scientific Explanation

Abstract

we introduce a new function, which is defined by replacing polynomials withpolynomial factorials in the expansion of exponential function denoted by  entitled as extorial function, an original and unique contribution. The identities that must be used with difference operators and factorials are mentioned. In the RL circuit, these identities are used to find solutions to the difference and discrete partial difference equations for heat and current flows. The above results are supported by numerical verifications. On the basis of the findings, the solution for current flow in the RL circuit is effectively derived after formulating the current flow as the discrete and fractional equations.