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Generalization
of Ostrowski’s
Type Inequality
Via Riemann-Liouville
Fractional
Integral and
Applications in
Numerical
Integration,
Probability
Theory and
Special Means
Faraz Mehmood (1,2) and Akhmadjon Soleev (1)
(1) Department
of Mathematics,
Samarkand State
University,
University
boulevard 15,
Samarkand
140104,
Uzbekistan
Email address:
faraz.mehmood@duet.edu.pk
Email address:
asoleev@yandex.com
/
asoleev@yandex.ru
(2) Department of
Mathematics, Dawood
University of
Engineering and
Technology, New M.
A. Jinnah Road,
Karachi-74800,
Pakistan
Doi :
https://doi.org/10.47013/17.1.10
Cited by :
Jordan J. Math &
Stat.,
17 (1) (2024),
161 - 178
PDF
Received on:
Dec. 19,
2022;
Accepted
on: May 3,
2023
Abstract. We apply
Riemann-Liouville
fractional
integral to get
a new
generalization
of Ostrowski’s
type integral
inequality. We
may prove new
estimates for
the remainder
term of the
midpoint’s,
trapezoid’s, &
Simpson’s
formulae as a
result of the
generalization.
Our estimates
are generalized
and recaptured
some previously
obtained
estimates.
Applications are
also deduced for
numerical
integration,
probability
theory and
special means.
Keywords: Fractional
Calculus,
Riemann-Liouville
fractional
integral
operator,
Ostrowski’s
inequality,
Error bounds,
Probability
density
function,
Numerical
integration,
Special means.
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