Abstract

This paper presents a new type of Gronwall-Bellman inequality, which arises from a class of integral equations with a mixture of nonsingular and singular integrals. The new idea is to use a binomial function to combine the known Gronwall-Bellman inequalities for integral equations having nonsingular integrals with those having singular integrals. Based on this new type of Gronwall-Bellman inequality, we investigate the existence and uniqueness of the solution to a fractional stochastic differential equation (SDE) with fractional order . Finally, the fractional type Fokker-Planck-Kolmogorov equation associated to the solution of the fractional SDE is derived using Itô’s formula.

Details

Title
A new type of the Gronwall-Bellman inequality and its application to fractional stochastic differential equations
Author
Wu, Qiong 1 

1  Department of Mathematics, Tufts University, 503 Boston Avenue, Medford, MA 02155 USA 
Publication year
2017
Publication date
Dec 2017
Publisher
Taylor & Francis Ltd.
e-ISSN
23311835
Source type
Scholarly Journal
Language of publication
English
DOI
https://doi.org/10.1080/23311835.2017.1279781
ProQuest document ID
2012877324
Copyright
© 2017 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license. This work is licensed under the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.