On more general inequalities for weighted generalized proportional Hadamard fractional integral operator with applications

Fractional calculus has been the target of the work of many mathematicians for more than a century. Some of these investigations are of inequalities and fractional integral operators. In this article, a novel fractional operator which is known as weighted generalized proportional Hadamard fractional operator with unknown attribute weight is proposed. First, a fractional formulation is constructed, which covers a subjective list of operators. With the aid of the above mentioned operators, numerous notable versions of Polya-Szego, Chebyshev and certain related variants are established. Meanwhile, new outcomes are introduced and new theorems are exhibited. Taking into account the novel generalizations, our consequences have a potential association with the previous results. Furthermore, we demonstrate the applications of new operator with numerous integral inequalities by inducing assumptions on weight function [??] and proportionality index [phi]. It is hoped that this research demonstrates that the suggested technique is efficient, computationally, very user-friendly and accurate. Keywords: weighted generalized proportional Hadamard fractional integrals; weighted Chebyshev inequality; Polya-Szego type inequality; Cauchy Schwartz inequality Mathematics Subject Classification: Primary: 47H09, 47H10, 90C39, 45D05, 34A12; Secondary: 54H25