Taylor’s Formula and Integral Inequalities for Conformable Fractional Derivatives

By Douglas R. Anderson. 2014

74 citations recorded by the source corpus.

We derive Taylor’s theorem using a variation of constants formula for conformable fractional derivatives. This is then employed to extend some recent and classical integral inequalities to the conformable fractional calculus, including the inequalities of Steffensen, Chebyshev, Hermite–Hadamard, Ostrowski, and Gruss.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/2f8891d29a646a92a94d6824c9a7c33b1b935fce

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In Applied Mathematics

1. Y. Chu
2. M. Adil Khan
3. Yousaf Khurshid
4. M. Sarıkaya
5. Sever Silvestru Dragomir
6. Artion Kashuri
7. Rozana Liko
8. Gohar Ali

In Modeling and Simulation

1. Y. Chu
2. M. Adil Khan
3. Yousaf Khurshid
4. Rozana Liko
5. M. Sarıkaya
6. Sever Silvestru Dragomir
7. T. Ali
8. Gohar Ali

Citations in the corpus

• Conformable Integral Inequalities of the Hermite-Hadamard Type in terms of GG- and GA-Convexities (2019, background): “Anderson [38] provided the conformable integral version of the HH inequality as follows.”
• Conformable fractional integral inequalities for GG- and GA-convex functions (2020, unknown): “Anderson [63] established the conformable integral version of the Hermite-Hadamard inequality as follows: α κ 2 − κ 1 ∫ κ2 κ1 h(x)dαx ≤ h(κ1) + h(κ2) 2 if α ∈ (0, 1] and h : [κ1, κ2]→ R is an α-fractional differentiable function such that Dα(h) is increasing.”
• Hermite–Hadamard type inequalities for conformable fractional integrals (2017, background): “Remark 7 Several important variants of Hermite–Hadamard inequality have been provided in the literature, such as the versions established by Anderson [5], Sarikaya et al.”
• Generalization of Hermite-Hadamard Type Inequalities via Conformable Fractional Integrals (2018, background): “Anderson [14] found the conformable integral version of the Hermite-Hadamard inequality as follows.”
• Conformable Fractional Integrals Versions of Hermite-Hadamard Inequalities and Their Generalizations (2018, methodology): “[21] D. R. Anderson, “Taylor’s formula and integral inequalities for conformable fractional derivatives,” in Contributions in Mathematics andEngineering, pp. 25–43, Springer, Cham, Switzerland, 2016.”