On Fractional Inequalities Using Generalized Proportional Hadamard Fractional Integral Operator

Abstract

The main objective of this paper is to use the generalized proportional Hadamard fractional integral operator to establish some new fractional integral inequalities for extended Chebyshev functionals. In addition, we investigate some fractional integral inequalities for positive continuous functions by employing a generalized proportional Hadamard fractional integral operator. The findings of this study are theoretical but have the potential to help solve additional practical problems in mathematical physics, statistics, and approximation theory.

Henri Poincaré’s Comment on Calculus and Albert Einstein’s Comment on Entropy: Mathematical Physics on the Tenth Anniversary of Axioms

“…A prospective similar development occurred a couple of decades ago when non-Abelian gauge theories emerged as QFTs for describing fundamental particle interactions. Recently, attention has turned to the application of Riemann-Liouville fractional calculus [6][7][8] to physics, including Tsallis non-additive entropy [9,10]. Statistical mechanics concerns mechanics (classical, quantum, special or general relativistic) and the theory of probabilities through the adoption of a specific entropic functional [11].…”

“…; Chesneau, C.; Khandagale, A.D. On Fractional Inequalities Using Generalized Proportional Hadamard Fractional Integral Operator. [8] A contribution is made to fractional calculus by using the generalized proportional Hadamard fractional integral operator to establish some new fractional integral inequalities for extended Chebyshev functionals. 5.…”

Grüss-type fractional inequality via Caputo-Fabrizio integral operator

“…Recently, many researchers have worked on fractional integral inequalities using the Riemann-Liouville, Hadamard and q-fractional integral, see [3,7,8,9,11,12,13,14,15,16,17,23,38]. In [16], Dahmani and et al gave the following fractional integral inequality using the Riemann-Liouville fractional integral.…”