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

Jagan Mohan Jonnalagadda

Abstract

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.

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

Abstract

This paper deals with fractional boundary value problems involving the Hilfer fractional differential operator of order and type . 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.

Paper Structure

This paper contains 3 sections, 10 theorems, 93 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Main Results

Key Result

Lemma 2.1

H1 For $a \in \mathbb{R}$, $\alpha > 0$, $0 \leq \beta \leq 1$ and $\mu > -1$, we have

Theorems & Definitions (23)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Definition 2.5
  • Definition 2.6
  • Definition 2.7
  • Lemma 2.1
  • Lemma 2.2
  • Lemma 2.3
  • ...and 13 more