On Some New Gruss Inequalities Concerning to Caputo k-fractional Derivative¨

Abstract

In this article, we establish some new integral inequalities on fractional calculus operator i.e. k-Caputo fractional derivative operator. As a consequence, we obtain new variety of fractional integral inequalities. Also we apply the Young’s inequality to find new versions of inequalities for the generalized fractional derivative. Such results for this new and generalized fractional derivative are very useful and worthwhile in the fields of differential equations and fractional differential calculus which has very deep connection with the real world problems. These results may motivate further research in different areas of pure and applied sciences.