Application of Mohand Transform in Solving Fractional Difference Equations

This study introduces the nabla discrete Mohand transform, specifically focusing on its fundamental properties along with its applications to fractional difference equations. It discusses fractional sum and difference evaluations using this transform alongside initial value problems in the relevant setting. The paper also links discrete fractional calculus to integral transforms by proving an important result related to the eigenfunction of the Caputo-type fractional difference operator \(\nabla _\alpha \) , where the eigenfunction is the discrete Mittag-Leffler function through the Mohand transforms. Beyond furthering the theoretical development of fractional calculus, this work also shows the use of the nabla discrete Mohand transform in practical applications. This has been demonstrated by solving applied problems from engineering, physics, and biology involving discrete systems. This research demonstrates the relevancy in applied engineering fields and arbitrary order difference equations.