TY - JOUR
T1 - Certain Chebyshev-type inequalities involving fractional conformable integral operators
AU - Rahman, Gauhar
AU - Ullah, Zafar
AU - Khan, Aftab
AU - Set, Erhan
AU - Nisar, Kottakkaran Sooppy
N1 - Publisher Copyright:
© 2019 by the authors.
PY - 2019/4/1
Y1 - 2019/4/1
N2 - Since an interesting functional by P.L. Chebyshev was presented in the year 1882, many results, which are called Chebyshev-type inequalities, have been established. Some of these inequalities were obtained by using fractional integral operators. Very recently, a new variant of the fractional conformable integral operator was introduced by Jarad et al. Motivated by this operator, we aim at establishing novel inequalities for a class of differentiable functions, which are associated with Chebyshev's functional, by employing a fractional conformable integral operator. We also aim at showing important connections of the results here with those including Riemann-Liouville fractional and classical integrals.
AB - Since an interesting functional by P.L. Chebyshev was presented in the year 1882, many results, which are called Chebyshev-type inequalities, have been established. Some of these inequalities were obtained by using fractional integral operators. Very recently, a new variant of the fractional conformable integral operator was introduced by Jarad et al. Motivated by this operator, we aim at establishing novel inequalities for a class of differentiable functions, which are associated with Chebyshev's functional, by employing a fractional conformable integral operator. We also aim at showing important connections of the results here with those including Riemann-Liouville fractional and classical integrals.
KW - Chebyshev's functional
KW - differentiable functions
KW - fractional conformable integral
KW - integral inequalities
KW - Riemann-Liouville (R-L) fractional integral
UR - https://www.scopus.com/pages/publications/85066442942
U2 - 10.3390/math7040364
DO - 10.3390/math7040364
M3 - Article
AN - SCOPUS:85066442942
SN - 2227-7390
VL - 7
JO - Mathematics
JF - Mathematics
IS - 4
M1 - 364
ER -