New integral inequalities and their applications to convex functions with a continuous Caputo fractional derivative

Volume 11, Issue 5, pp 658--671 http://dx.doi.org/10.22436/jnsa.011.05.07
Publication Date: March 31, 2018 Submission Date: June 14, 2017 Revision Date: August 19, 2017 Accteptance Date: October 28, 2017

Authors

Bashir Ahmad - Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. Mohamed Jleli - Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh, 11451, Saudi Arabia. Bessem Samet - Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh, 11451, Saudi Arabia.


Abstract

We say that a function \(f:[a,b]\to \mathbb{R}\) is \((\varphi,\delta)\)-Lipschitzian, where \(\delta\geq 0\) and \(\varphi:[0,\infty)\to [0,\infty)\), if \[ |f(x)-f(y)|\leq \varphi(|x-y|)+\delta,\quad (x,y)\in [a,b]\times [a,b]. \] In this work, some Hadamard's type inequalities are established for the class of \((\varphi,\delta)\)-Lipschitzian mappings. Moreover, some applications to convex functions with a continuous Caputo fractional derivative are also discussed.


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ISRP Style

Bashir Ahmad, Mohamed Jleli, Bessem Samet, New integral inequalities and their applications to convex functions with a continuous Caputo fractional derivative, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 5, 658--671

AMA Style

Ahmad Bashir, Jleli Mohamed, Samet Bessem, New integral inequalities and their applications to convex functions with a continuous Caputo fractional derivative. J. Nonlinear Sci. Appl. (2018); 11(5):658--671

Chicago/Turabian Style

Ahmad, Bashir, Jleli, Mohamed, Samet, Bessem. "New integral inequalities and their applications to convex functions with a continuous Caputo fractional derivative." Journal of Nonlinear Sciences and Applications, 11, no. 5 (2018): 658--671


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