Fractional-order integral inequalities of the Milne type

This thesis examines Milne-type inequalities using the Absolute Value, Hölder, Power Mean, and Young inequalities. The first part of the thesis covers a broad history of inequalities, the second part includes definitions, theorems, and examples, the third part extends the definition using Riemann–Liouville and Caputo–Fabrizio operators, and the fourth part uses existing lemmas to derive Milne-type integral inequalities related to convex functions. The fifth part provides discussions and conclusions. The primary goal of this thesis is to examine Milne-type fractional integral inequalities from a broad perspective, derive new inequalities using different fractional operators, and reach upper bounds on new applications of these inequalities.