New Multiplicative Mid-Point and Trapezoidal Fractional Integral Inequalities

Abstract

In this thesis the mid-point fractional integral inequalities and multiplicative trapezoidal inequalities are thoroughly examined. We construct new lemmas and provide their pre cise estimations for differentiable and twice differentiable functions using fractional and k-fractional integrals. Furthermore, new bounds via Holder inequalities are obtained to ¨ demonstrate the strength, flexibility and usefulness of the suggested conclusions in the context of fractional calculus. A variety of examples are analyzed and their graphical rep resentations drawn for easier interpretation in order to validate the theoretical findings. In addition to contributing to our understanding of fractional integral inequalities, this re search provides new opportunities for future investigation into fractional calculus and its uses in science and engineering