Some parameterized Simpson-, midpoint- and trapezoid-type inequalities for generalized fractional integrals

Abstract

In this paper, we first obtain an identity for differentiable mappings. Then, we establish some new generalized inequalities for differentiable convex functions involving some parameters and generalized fractional integrals. We show that these results reduce to several new Simpson-, midpoint- and trapezoid-type inequalities. The results given in this study are the generalizations of results proved in several earlier papers.

A Study on the New Class of Inequalities of Midpoint-Type and Trapezoidal-Type Based on Twice Differentiable Functions with Conformable Operators

“…For instance, biological population model [11], electrical circuits [12], viscous fluid and their semianalytical solutions [13], fractional gas dynamics [14], and fractal modeling of traffic flow [15] are applied examples of the application of fractional operators. Further, it is stated that fractional systems provide some numerical outcomes that are more appropriate than those given by integer-order systems [16,17].…”

Fractional Simpson-like Inequalities with Parameter for Differential s-tgs-Convex Functions

“…Convexity has a close relation in the development of the theory of inequalities, of which it plays an important role in the study of qualitative properties of solutions of ordinary, partial, and integral differential equations as well as in numerical analysis, which is used for establishing the estimates of the errors for quadrature rules; see [7][8][9][10][11][12][13][14][15][16][17][18].…”

New Midpoint-type Inequalities of Hermite-Hadamard Inequality with Tempered Fractional Integrals

“…In recent years, fractional integration and derivatives have become a topic with applications in many fields such as mathematical physics, electrotechnics, materials science, biomedical engineering, fluid dynamics, and finance. One can find the papers referenced in [10][11][12][13][14] about fractional calculus.…”