On the Gronwall Inequality via Discrete Fractional Calculus رسالة ماجستير

Abstract

On the Gronwall Inequality via Discrete Fractional Calculus Dana Emad Mahmoud Atiya Tn this work, Gronwall’s inequality for h-discrete calculus with the nabla opera- tor on h% has been proved. We illustrate our results in the context of initial value problem (IVP). Moreover, Gronwall’s inequality for discrete calculus on Z has been verified. For this purpose the equivalence of an initial value problem for a discrete fractional equation and a discrete fractional sum equation on Z and on hZ have been considered, and the h-discrete Mittag-Leffler function in term of »Enw and Fn have been defined. Then an explicit solution have been given for linear discrete fractional sum equation.