具有rabotnov分数阶指数核的一般分数阶积分的新型chebyshev型不等式

IF 3.3 3区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Fractals-Complex Geometry Patterns and Scaling in Nature and Society Pub Date : 2023-11-08 DOI:10.1142/s0218348x23501268

LU-LU GENG, XIAO-JUN YANG

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引用次数: 0

摘要

本文首先在[公式:见文]和[公式:见文]为同步函数的条件下，提出了两个与一般分数阶(yang - abdel - ati - cattani)积分与Rabotnov分数阶-指数核相关的chebyshev型不等式。并利用数学归纳法，证明了[公式:见文]是[公式:见文]正递增函数时的一个新的切比雪夫不等式。最后，在[公式:见文]和[公式:见文]为单调函数的条件下，利用Rabotnov分数指数核的一般分数阶积分，引入了一个新的chebyshev型不等式。

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

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 [Formula: see text] and [Formula: see text] are synchronous functions. What is more, by the mathematical induction, we prove a new Chebyshev-type inequality in the case that [Formula: see text] be [Formula: see text] 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 [Formula: see text] and [Formula: see text] are monotonic functions.

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来源期刊

Fractals-Complex Geometry Patterns and Scaling in Nature and Society 数学-数学跨学科应用

CiteScore

7.40

自引率

23.40%

发文量

319

审稿时长

>12 weeks

期刊介绍： The investigation of phenomena involving complex geometry, patterns and scaling has gone through a spectacular development and applications in the past decades. For this relatively short time, geometrical and/or temporal scaling have been shown to represent the common aspects of many processes occurring in an unusually diverse range of fields including physics, mathematics, biology, chemistry, economics, engineering and technology, and human behavior. As a rule, the complex nature of a phenomenon is manifested in the underlying intricate geometry which in most of the cases can be described in terms of objects with non-integer (fractal) dimension. In other cases, the distribution of events in time or various other quantities show specific scaling behavior, thus providing a better understanding of the relevant factors determining the given processes. Using fractal geometry and scaling as a language in the related theoretical, numerical and experimental investigations, it has been possible to get a deeper insight into previously intractable problems. Among many others, a better understanding of growth phenomena, turbulence, iterative functions, colloidal aggregation, biological pattern formation, stock markets and inhomogeneous materials has emerged through the application of such concepts as scale invariance, self-affinity and multifractality. The main challenge of the journal devoted exclusively to the above kinds of phenomena lies in its interdisciplinary nature; it is our commitment to bring together the most recent developments in these fields so that a fruitful interaction of various approaches and scientific views on complex spatial and temporal behaviors in both nature and society could take place.