Estimation of Unknown Function of a Class of Integral Inequalities with pth Power

DOI

10.2991/emim-15.2015.118How to use a DOI?

Keywords

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

Abstract

Fractional differential equations and fractional integral equations have gained considerable importance and attention due to their applications in many engineering and scientific disciplines. Gronwall-Bellman inequalities are important tools in the study of existence, uniqueness, boundedness, stability and other qualitative properties of solutions of Fractional differential equations and fractional integral equations. In this paper, we discuss a class of integral inequalities with pth power, which includes a nonconstant term outside the integrals. Using the definitions and properties of modified Riemann-Liouville fractional derivative and Riemann-Liouville fractional integral, the upper bounds of the unknown function is estimated explicitly. The derived result can be applied in the study of qualitative properties 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  - Yusong Lu
AU  - Wusheng Wang
AU  - Hua Zhong
PY  - 2015/04
DA  - 2015/04
TI  - Estimation of Unknown Function of a Class of Integral Inequalities with pth Power
BT  - Proceedings of the 2015 International Conference on Education, Management, Information and Medicine
PB  - Atlantis Press
SP  - 596
EP  - 599
SN  - 2352-5428
UR  - https://doi.org/10.2991/emim-15.2015.118
DO  - 10.2991/emim-15.2015.118
ID  - Lu2015/04
ER  -