NOVEL CHEBYSHEV-TYPE INEQUALITIES FOR THE GENERAL FRACTIONAL-ORDER INTEGRALS WITH THE RABOTNOV FRACTIONAL EXPONENTIAL KERNEL

Lu-Lu Geng and Xiao-Jun Yang
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Lu-Lu Geng: School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu 221116, P. R. China†State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, P. R. China
Xiao-Jun Yang: School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu 221116, P. R. China†State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, P. R. China‡Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80257, Jeddah 21589, Saudi Arabia§Department of Mathematics, College of Science Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea

FRACTALS (fractals), 2023, vol. 31, issue 09, 1-9

Abstract: In this paper, we first propose two Chebyshev-type inequalities associated with the general fractional-order (Yang–Abdel–Aty–Cattani) integrals with the Rabotnov fractional-exponential kernel under the condition that μ and ν are synchronous functions. What is more, by the mathematical induction, we prove a new Chebyshev-type inequality in the case that (μi)i=1,…,n be n positive increasing functions. Finally, we introduce a novel Chebyshev-type inequality via the general fractional-order integrals with the Rabotnov fractional-exponential kernel under the condition that μ and ν are monotonic functions.

Keywords: Rabotnov Fractional-exponential Function; General Fractional-order Integrals; Chebyshev Functional; Synchronous Function; Monotonic Function (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23501268

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