Fundamental Theorems in Discrete Fractional Calculus Using Nabla Operator


M. Sebasti Jeya Pushpam
Department of Mathematics, Auxilium College of Arts & Science for Women, Rengunathapuram, Tamil Nadu


The purpose of this work is to develop the theory of discrete version of fundamental theorems of l-nabla integration. This theory has been established through ∞-order nabla-l integrable function. This theory is then applied to arrive several fundamental theorems and examples on fractional order sums in the field of discrete fractional calculus. We have derived some definitions and summation formula arrived by inverse of ∇l and also derived theorems on integer order. Along with this, we have derived theorems on fractional order nabla integration with suitable examples.

October 19, 2023