Estimation of Unknown Function of a Class of Integral Inequalities

DOI

10.2991/emim-15.2015.82How to use a DOI?

Keywords

Iterated integral inequality; Integral inequality technique; Modified Riemann-Liouville fractional derivative; Riemann-Liouville fractional integral; Estimation of solution

Abstract

It is well known that differential equations, integral equations and integral-differential equations have gained considerable importance and attention due to their applications in many engineering and scientific disciplines as the mathematical modeling of systems and processes in the fields of physical, mechanics, chemistry, aerodynamics, and the electrodynamics of complex mediums, etc. Gronwall-Bellman inequality is an important tool in the study of existence, uniqueness, boundedness, and other qualitative properties of solutions of differential equations and integral equation. In this paper, we discuss we establish a class of retarded iterated integral inequalities, which includes a nonconstant term outside the integrals. By integral inequality technique, the upper bounds of the embedded unknown function is estimated explicitly. The derived result can be applied in the study of solutions of fractional integral equations.

Copyright

© 2015, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Hua Zhong
AU  - Wusheng Wang
AU  - Lele Fan
PY  - 2015/04
DA  - 2015/04
TI  - Estimation of Unknown Function of a Class of Integral Inequalities
BT  - Proceedings of the 2015 International Conference on Education, Management, Information and Medicine
PB  - Atlantis Press
SP  - 421
EP  - 424
SN  - 2352-5428
UR  - https://doi.org/10.2991/emim-15.2015.82
DO  - 10.2991/emim-15.2015.82
ID  - Zhong2015/04
ER  -