On Chebyshev and Riemann-Liouville Fractional Inequalities in q-Calculus
Stephen. N. Ajega-Akem *
Department of Mathematics, Faculty of Mathematical Sciences, University for Development Studies, P.O. Box 24 Navrongo Campus, Navrongo, Upper East, Ghana.
Mohammed M. Iddrisu
Department of Mathematics, Faculty of Mathematical Sciences, University for Development Studies, P.O. Box 24 Navrongo Campus, Navrongo, Upper East, Ghana.
Kwara Nantomah
Department of Mathematics, Faculty of Mathematical Sciences, University for Development Studies, P.O. Box 24 Navrongo Campus, Navrongo, Upper East, Ghana.
*Author to whom correspondence should be addressed.
Abstract
This paper presents some new inequalities on Fractional calculus in the context of q-calculus. Fractional calculus generalizes the integer order differentiation and integration to derivatives and integrals of arbitrary order. In other words, Fractional calculus explores integrals and derivatives of functions that involve non-integer order(s). Quantum calculus (q-Calculus) on the other hand focuses on investigations related to calculus without limits and in recent times, it has attracted the interest of many researchers due to its high demand of mathematics to model complex systems in nature with anomalous dynamics. This paper thus establishes some new extensions of Chebyshev and Riemann-Liouville fractional integral inequalities for positive and increasing functions via q-Calculus.
Keywords: Chebyshev inequality, riemann-liouville, fractional calculus, q-Calculus