Wirtinger-Type Inequalities Involving Tempered Ψ-Fractional Derivatives with Applications

In this work, we explore Wirtinger-type inequalities involving tempered Ψ-Caputo fractional derivatives by utilizing Taylor’s formula. We establish more general inequalities for the same operator in Lp norms for p>1 by using Hölder’s inequality. Special cases are discussed in the form of remarks by highlighting their relationships with the existing literature. The derived results are also verified through illustrative examples, including tables and graphs. Moreover, applications of the obtained inequalities are discussed in the context of arithmetic and geometric means.