Studies in fractal-fractional operators with examples

被引：2

作者：

Ibrahim, Rabha W. ^{[1
,2
]}

机构：

[1] Istanbul Okan Univ, Fac Engn & Nat Sci, Adv Comp Lab, Istanbul, Turkiye

[2] Al Ayen Univ, Sci Res Ctr, Informat & Commun Technol Res Grp, Thi Qar, Iraq

来源：

EXAMPLES AND COUNTEREXAMPLES | 2024年 / 6卷

关键词：

Fractional calculus; Fractal calculus; Fractional difference operator; Fractal-fractional differential operator;

D O I：

10.1016/j.exco.2024.100148

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By using the generalization of the gamma function (p-gamma function: Gamma p(.)), we introduce a generalization of the fractal-fractional calculus which is called p-fractal fractional calculus. We extend the proposed operators into the symmetric complex domain, specifically the open unit disk. Normalization for each operator is formulated. This allows us to explore the most important geometric properties. Examples are illustrated including the basic power functions.

引用

页数：5

共 50 条

[41] VARIATIONAL FORMULATIONS FOR A COUPLED FRACTAL-FRACTIONAL KdV SYSTEM
Guan, Yingzi
Gepreel, Khaled A.
He, Ji-Huan
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2024, 32 (03)
[42] On fractal-fractional Covid-19 mathematical model
Khan, Hasib
Ahmad, Farooq
Tunc, Osman
Idrees, Muhammad
CHAOS SOLITONS & FRACTALS, 2022, 157
[43] A FRACTAL-FRACTIONAL TSUNAMI MODEL CONSIDERING NEAR-SHORE FRACTAL BOUNDARY
Wang, Yan
Hou, Weifan
Gepreel, Khaled
Li, Hongju
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2024, 32 (02)
[44] Fractal-fractional estimations of Bullen-type inequalities with applications
Butt, Saad Ihsan
Yasin, Muhammad Umar
Tipuric-Spuzevic, Sanja
Bin-Mohsin, Bandar
AIN SHAMS ENGINEERING JOURNAL, 2024, 15 (12)
[45] Dynamic analysis on Liu system under fractal-fractional differentiation
Gandhimathi, R.
Gowrisankar, A.
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS, 2024,
[46] Fractal-fractional neuro-adaptive method for system identification
Zuniga-Aguilar, C. J.
Gomez-Aguilar, J. F.
Romero-Ugalde, H. M.
Jahanshahi, Hadi
Alsaadi, Fawaz E.
ENGINEERING WITH COMPUTERS, 2022, 38 (04) : 3085 - 3108
[47] NEW CLASS OF VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITH FRACTAL-FRACTIONAL OPERATORS: EXISTENCE, UNIQUENESS AND NUMERICAL SCHEME
Araz, Seda Igret
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2021, 14 (07): : 2297 - 2309
[48] A mathematical model of transmission cycle of CC-Hemorrhagic fever via fractal-fractional operators and numerical simulations
Etemad, Sina
Tellab, Brahim
Zeb, Anwar
Ahmad, Shabir
Zada, Akbar
Rezapour, Shahram
Ahmad, Hijaz
Botmart, Thongchai
RESULTS IN PHYSICS, 2022, 40
[49] A New Class of Generalized Fractal and Fractal-Fractional Derivatives with Non-Singular Kernels
Hattaf, Khalid
FRACTAL AND FRACTIONAL, 2023, 7 (05)
[50] The complex dynamical behaviour of fractal-fractional forestry biomass system
Kumar, Parveen
Kumar, Sunil
Alkahtani, Badr Saad T.
Alzaid, Sara S.
APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING, 2024, 32 (01):

← 1 2 3 4 5 →