검색
Article Search

JMB Journal of Microbiolog and Biotechnology

OPEN ACCESS eISSN 0454-8124
pISSN 1225-6951
QR Code

Article

Kyungpook Mathematical Journal 2020; 60(1): 211-222

Published online March 31, 2020

Copyright © Kyungpook Mathematical Journal.

On Some Fractional Quadratic Integral Inequalities

Ahmed M. A. El-Sayed, Hind H. G. Hashem∗

Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt
e-mail : amasayed@alexu.edu.eg
Department of Mathematics, Faculty of Science, Qassim University, Buraidah, Saudi Arabia
e-mail : hendhghashem@yahoo.com

Received: September 5, 2018; Revised: March 17, 2019; Accepted: March 18, 2019

Abstract

Integral inequalities provide a very useful and handy tool for the study of qualitative as well as quantitative properties of solutions of differential and integral equations. The main object of this work is to generalize some integral inequalities of quadratic type not only for integer order but also for arbitrary (fractional) order. We also study some inequalities of Pachpatte type.

Keywords: fractional-order integral inequality, fractional quadratic integral equations, Bellman-Gronwall’s inequality, inequality of Pachpatte type