On new fractional integral inequalities using Marichev–Saigo–Maeda operator

Abstract

Generalizations of fractional integral inequalities were introduced by many authors. The aim of our investigation is to establish some new fractional integral inequalities using Marichev–Saigo–Maeda (MSM) fractional integral operator for convex function. Further, we obtain some more fractional integral inequalities of Grüss type using MSM operator.

New Inequalities Using Multiple Erdélyi–Kober Fractional Integral Operators

“…The existing classical inequalities cited herein can be obtained as special cases of the inequalities produced in this paper. As a result, as was discussed in Section 2 of this article, these inequalities can be reduced in terms of the other non-trivial integral inequalities involving Saigo, M-S-M, R-L [5,10], and so forth. M-E-K fractional integral operators have been effectively used by authors to investigate a novel special function representation [29,30].…”

“…We can compute the required result as stated in Theorem 1 with the addition of inequality (10) and inequality (12).…”

“…Moreover, in the past few years, fractional integral inequalities have emerged as one of the most practical and extensive instruments for the advancement of numerous topics in both pure and applied mathematics [1]. Therefore, several scholars have presented a variety of generalized inequalities involving fractional integral operators [2][3][4][5][6][7][8][9][10][11]. In addition to its generalizations and extensions in one or more variables, fractional calculus covers a variety of important problems involving unique mathematical physics functions and offers various potentially helpful methods for solving differential and integral equations [12].…”