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Jagan Mohan Jonnalagadda

Publications and source records attributed to Jagan Mohan Jonnalagadda.

8 recordsLinked to original sources
arXiv2023

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 $1 < α\leq 2$ and type $0 \leq β\leq 1$. 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.

math.GM↗
arXiv2022

Green's Functions and Existence of Solutions of Nonlinear Fractional Implicit Difference Equations with Dirichlet Boundary Conditions

This article is devoted to deduce the expression of the Green's function related to a general constant coefficients fractional difference equation coupled to Dirichlet conditions. In this case, due to the points where some of the fractional operators is applied, we are in presence of a implicit fractional difference equation. Such property makes it more complicated to calculate and manage the expression of the Green's function. Such expression, on the contrary to the explicit case where it follows from finite sums, is deduced from series of infinity terms. Such expression will be deduced from the Laplace transform on the time scales of the integers. Finally, we prove two existence results for nonlinear problems, via suitable fixed point theorems.

math.CA↗
arXiv2021

A Remark on the Memory Property of Fractional Difference Operators

Fractional difference operators possess nonlocal structure which largely affects and complicates the qualitative analysis of fractional difference equations. In this article, we discuss the effect of this memory property on asymptotic behaviour of solutions of nabla fractional difference equations.

math.GM↗
arXiv2019

On a Nabla Fractional Boundary Value Problem with General Boundary Conditions

In this article, we consider a nabla fractional boundary value problem with general boundary conditions. Brackins \& Peterson \cite{Br} gave an explicit expression for the corresponding Green's function. Here, we show that this Green's function is nonnegative and obtain an upper bound for its maximum value. Since the expression for the Green's function is complicated, derivation of its properties may not be straightforward. For this purpose, we use a few properties of fractional nabla Taylor monomials. Using the Green's function, we will then develop a Lyapunov-type inequality for the nabla fractional boundary value problem.

math.CA↗
arXiv2018

Lyapunov-Type Inequalities for Discrete Riemann-Liouville Fractional Boundary Value Problems

In this article we establish a few Lyapunov-type inequalities for two-point discrete fractional boundary value problems involving Riemann-Liouville type backward differences. To illustrate the applicability of established results, we obtain criteria for the nonexistence of nontrivial solutions and estimate lower bounds for eigenvalues of the corresponding eigenvalue problems. We also apply these inequalities to deduce criteria for the nonexistence of real zeros of certain discrete Mittag-Leffler functions.

math.CA↗