Numerical Computation of Exponential Functions of Nabla Fractional Calculus

In this article, we illustrate the asymptotic behaviour of exponential functions of nabla fractional calculus. For this purpose, we propose a novel matrix technique to compute these functions numerically

A Short Note on Lyapunov Type Inequalities for Hilfer Fractional Boundary Value Problems

This paper deals with fractional boundary value problems involving the Hilfer fractional differential operator of order $1 < \alpha \leq 2$ and type $0 \leq \beta \leq 1$. We derive the corresponding Lyapunov-type inequalities for two prominent classes of Hilfer fractional boundary value problems (HFBVPs) involving separated and anti-periodic boundary conditions. For this purpose, we construct the associated Green's functions and deduce their important properties

Uniqueness and stability of solutions for a coupled system of nabla fractional difference boundary value problems

In this article, we obtain sufficient conditions on existence, uniqueness and Ulam–Hyers stability of solutions for a coupled system of two-point nabla fractional difference boundary value problems, using Banach, Brouwer fixed point theorems and Urs’s approach. Further, we illustrate the applicability of established results through an example.Publisher's Versio