On Some Fractional Integral Inequalities Involving Caputo–Fabrizio Integral Operator

Abstract

In this paper, we deal with the Caputo–Fabrizio fractional integral operator with a nonsingular kernel and establish some new integral inequalities for the Chebyshev functional in the case of synchronous function by employing the fractional integral. Moreover, several fractional integral inequalities for extended Chebyshev functional by considering the Caputo–Fabrizio fractional integral operator are discussed. In addition, we obtain fractional integral inequalities for three positive functions involving the same operator.

A Method to solve ordinary fractional differential equations using Elzaki and Sumudu transform

“…Recently, The Caputo and Caputo-Fabrizio fractional operators have recently become quite popular among mathematicians in applied fields. We cite for additional information [7,8,9,10,11,12].…”

Pólya–Szegö Integral Inequalities Using the Caputo–Fabrizio Approach

“…Wang et al[30] obtained the Hermite-Hadamard inequalities by employing the Caputo-Fabrizio fractional operator. In[31], Chinchane et al dealt with the Caputo-Fabrizio fractional integral operator with a nonsingular kernel and established some new integral inequalities for the Chebyshev functional, in the case of synchronous function, by employing the fractional integral. Jain et al[24] established some new Pólya-Szegö inequality fractional integral inequalities by considering Riemann-Liouville-type fractional integral operators.…”