Entropy Interpretation of Hadamard Type Fractional Operators: Fractional Cumulative Entropy

被引：7
作者：
Tarasov, Vasily E. [1 ,2 ]
机构：
[1] Lomonosov Moscow State Univ, Skobeltsyn Inst Nucl Phys, Moscow 119991, Russia
[2] Natl Res Univ, Moscow Aviat Inst, Dept Phys, Moscow 125993, Russia
来源：
ENTROPY | 2022年 / 24卷 / 12期
关键词：
fractional calculus; fractional integrals; Hadamard-type fractional pperator; entropy; cummulative entropy; fractional entropy; DIFFERENTIAL-EQUATIONS; PROBABILITY INTERPRETATION; GEOMETRICAL INTERPRETATION; PHYSICAL INTERPRETATION; ANOMALOUS DIFFUSION; DERIVATIVES; INTEGRATION; CALCULUS; RELAXATION; DYNAMICS;
D O I：
10.3390/e24121852
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
Interpretations of Hadamard-type fractional integral and differential operators are proposed. The Hadamard-type fractional integrals of function with respect to another function are interpreted as an generalization of standard entropy, fractional entropies and cumulative entropies. A family of fractional cumulative entropies is proposed by using the Hadamard-type fractional operators.
引用
收藏
页数：18
相关论文
共 99 条
[11]   PHYSICAL AND GEOMETRICAL INTERPRETATION OF GRUNWALD-LETNIKOV DIFFERINTEGRALS: MEASUREMENT OF PATH AND ACCELERATION [J].
Cioc, Radoslaw .
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2016, 19 (01) :161-172
[12]   On cumulative entropies [J].
Di Crescenzo, Antonio ;
Longobardi, Maria .
JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2009, 139 (12) :4072-4087
[13]   Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type [J].
Diethelm, Kai .
ANALYSIS OF FRACTIONAL DIFFERENTIAL EQUATIONS: AN APPLICATION-ORIENTED EXPOSITION USING DIFFERENTIAL OPERATORS OF CAPUTO TYPE, 2010, 2004 :3-+
[14]  
Erdelyi A., 1953, Higher Transcendental Functions
[15]   Tempered and Hadamard-Type Fractional Calculus with Respect to Functions [J].
Fahad, Hafiz Muhammad ;
Fernandez, Arran ;
Rehman, Mujeeb Ur ;
Siddiqi, Maham .
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2021, 18 (04)
[16]  
Fix GJ, 2002, APPL MATH LETT, V15, P907
[17]   On Caputo modification of the Hadamard fractional derivatives [J].
Gambo, Yusuf Y. ;
Jarad, Fahd ;
Baleanu, Dumitru ;
Abdeljawad, Thabet .
ADVANCES IN DIFFERENCE EQUATIONS, 2014,
[18]   A Note on Hadamard Fractional Differential Equations with Varying Coefficients and Their Applications in Probability [J].
Garra, Roberto ;
Orsingher, Enzo ;
Polito, Federico .
MATHEMATICS, 2018, 6 (01)
[19]   A generalization of the Lomnitz logarithmic creep law via Hadamard fractional calculus [J].
Garra, Roberto ;
Mainardi, Francesco ;
Spada, Giorgio .
CHAOS SOLITONS & FRACTALS, 2017, 102 :333-338
[20]   On some operators involving Hadamard derivatives [J].
Garra, Roberto ;
Polito, Federico .
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2013, 24 (10) :773-782
12345678910