Minkowski-type inequalities using generalized proportional Hadamard fractional integral operators

Abstract

The main objective of present investigation is to obtain some Minkowski-type fractional integral inequalities using generalised proportional Hadamard fractional integral operators which is introduced by Rahman et al. in the paper (Certain inequalities via generalized proportional Hadamard fractional integral operators), Advances in Differential Equations, 2019, 454(2019). In addition, we establish some other fractional integral inequalities for positive and continuous functions.

Study of Uniqueness and Ulam-Type Stability of Abstract Hadamard Fractional Differential Equations of Sobolev Type via Resolvent Operators

“…In Refs. [33,34], the authors derived fractional inequalities by utilizing a Hadamard fractional operator. This operator was employed to establish the existence and uniqueness of solutions for fractional differential equations.…”

On Fractional Inequalities Using Generalized Proportional Hadamard Fractional Integral Operator

“…Later, Lasada and Niteto proposed certain properties of fractional derivatives without a singular kernel [49]. Nale et al and Rahaman et al [44,50] investigated some Minkowskitype inequalities and other integral inequalities by considering the generalized proportional Hadamard fractional integral operator. Kukushkin [51] examined the final terms of a differential operator with a fractional integro-differential operator composition on a bounded domain of n-dimensional Euclidean space, as well as on the real axis.…”