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- Title
Simpson Type Inequalities for Twice-differentiable Functions Arising from Tempered Fractional Integral Operators.
- Authors
Jieyin Cai; Bin Wang; Tingsong Du
- Abstract
Simpson inequalities for first-order differentiable convex functions and various fractional integrals have been studied extensively. However, Simpson type inequalities for twice-differentiable functions are researched slightly. Therefore, in the present paper, we endeavor to study fractional inequalities of Simpson type for twice-differentiable convex functions. To achieve this goal, we establish a new twicedifferentiable Simpson's identity by using tempered fractional integral operators. Based upon it, we prove several fractional Simpson type inequalities whose second derivatives in absolute value are convex. Finally, we give some examples to illustrate the correctness of the obtained results.
- Subjects
FRACTIONAL integrals; INTEGRAL operators; ABSOLUTE value; CONVEX functions; DIFFERENTIABLE functions
- Publication
IAENG International Journal of Applied Mathematics, 2024, Vol 54, Issue 5, p831
- ISSN
1992-9978
- Publication type
Article