New Generalized Extended Hardy-type Dynamic Inequalities on Time Scales

This research will demonstrate several novel dynamic inequalities of the Hardy type on time scales. These inequalities will be generalized and expanded. Several new integral and difference inequalities are produced as a consequence of our findings in both continuous and discrete scenarios. The dynamic Holder ¨ inequality, the integration by parts formula on time scales, and Keller’s chain rule on time scales will be utilized to demonstrate the primary findings. To apply the primary findings, we shall employ discrete calculus, quantum calculus, and continuous calculus and treat them as special cases.