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/).
Cite this article
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 -