Retraction
Derivative with two fractional orders: A new avenue of investigation toward revolution in fractional calculus
Paper Information
Record ID:
25494
Author(s):
Journal:
Publication Date:
October 24, 2016
Retraction Date:
January 18, 2021
(4.8 years years ago)
Subject:
Broad Categories:
Mathematics
Mathematics
Specific Fields:
Mathematics
Mathematics
Country:
đżđŠ South AfricaArticle Type:
Publisher:
Springer
Open Access:
Yes
PubMed ID:
Not indexed in PubMed
Retraction PubMed ID:
Not indexed in PubMed
Retraction Details
Retraction Reasons:
Nature of Retraction:
Retraction
Retraction Notice:
10.1140/epjp/s13360-020-00965-wAdditional Notes:
see also: https://pubpeer.com/publications/B407AFE30CFC7A36FF6240FE344F8E;
Citations (48)
48
Total Citations4
Post-Retraction(8.3%)
44
Pre-Retraction0
Same DayPost-Retraction Citation Analysis
0
Within 30 days
1
Within 1 year
1
After 2+ years
1443
Days since retraction (latest)
Paper citing Derivative with two fractional orders: A new avenu...
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Analysis of nonlinear fractional optimal control systems described by delay VolterraâFredholm integral equations via a new spectral collocation method
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Chaos Solitons & Fractals
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13 citations
13 citations
567 days after retraction
NUMERICAL ANALYSIS OF NEWLY DEVELOPED FRACTAL-FRACTIONAL MODEL OF CASSON FLUID WITH EXPONENTIAL MEMORY
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26 citations
26 citations
372 days after retraction
Common fixed point results for multi-valued mappings in complex-valued double controlled metric spaces and their applications to the existence of solution of fractional integral inclusion systems
Pari Amiri, Hojjat Afshari
Chaos Solitons & Fractals
Published: Dec 2021
1 citation
1 citation
327 days after retraction
Retraction Note to: Derivative with two fractional orders: A new avenue of investigation toward revolution in fractional calculus
Abdon Atangana
The European Physical Journal Plus
Open Access
Published: Jan 2021
17 days before retraction
New Aspects of Bloch Model Associated with Fractal Fractional Derivatives
Ali AkgĂŒl, Ishfaq Ahmad Mallah, Subhash Alha
Nonlinear Engineering
Open Access
Published: Jan 2021
1 citation
1 citation
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Role of fractalâfractional derivative on ferromagnetic fluid via fractal Laplace transform: A first problem via fractalâfractional differential operator
Kashif Ali Abro
European Journal of Mechanics - B/Fluids
Published: Sep 2020
60 citations
60 citations
137 days before retraction
A POD-based reduced-order Crank-Nicolson/fourth-order alternating direction implicit (ADI) finite difference scheme for solving the two-dimensional distributed-order Riesz space-fractional diffusion equation
Mostafa Abbaszadeh, Mehdi Dehghan
Applied Numerical Mathematics
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41 citations
41 citations
167 days before retraction
A novel mathematical approach of COVID-19 with non-singular fractional derivative
Sachin Kumar, Jinde Cao, Mahmoud AbdelâAty
Chaos Solitons & Fractals
Open Access
Published: Jul 2020
32 citations
32 citations
201 days before retraction
THE NUMERICAL TREATMENT OF NONLINEAR FRACTALâFRACTIONAL 2D EMDENâFOWLER EQUATION UTILIZING 2D CHELYSHKOV POLYNOMIALS
M. Hosseininia, Mohammad Heydari, Z. Avazzadeh
Fractals
Open Access
Published: May 2020
17 citations
17 citations
257 days before retraction
NUMERICAL TREATMENT OF THE SPACEâTIME FRACTALâFRACTIONAL MODEL OF NONLINEAR ADVECTIONâDIFFUSIONâREACTION EQUATION THROUGH THE BERNSTEIN POLYNOMIALS
Mohammad Heydari, Z. Avazzadeh, Yin Yang
Fractals
Open Access
Published: May 2020
19 citations
19 citations
257 days before retraction
An approximate approach for the generalized variable-order fractional pantograph equation
Z. Avazzadeh, Mohammad Heydari, Mohammad Reza Mahmoudi
Alexandria Engineering Journal
Open Access
Published: Mar 2020
17 citations
17 citations
313 days before retraction
Fractional derivatives with singular kernels
XiaoâJun Yang, Feng Gao, Yang Ju
Elsevier eBooks
Published: Jan 2020
5 citations
5 citations
383 days before retraction
Fractional derivatives with nonsingular kernels
XiaoâJun Yang, Feng Gao, Yang Ju
Elsevier eBooks
Published: Jan 2020
5 citations
5 citations
383 days before retraction
Generalized Model of Blood Flow in a Vertical Tube with Suspension of Gold Nanomaterials: Applications in the Cancer Therapy
Anees Imtiaz, Oi-Mean Foong, Aamina Aamina et al. (6 authors)
Computers, materials & continua/Computers, materials & continua (Print)
Open Access
Published: Jan 2020
16 citations
16 citations
383 days before retraction
A reduced order finite difference method for solving space-fractional reaction-diffusion systems: The Gray-Scott model
Mostafa Abbaszadeh, Mehdi Dehghan
The European Physical Journal Plus
Published: Dec 2019
27 citations
27 citations
414 days before retraction
Chebyshev polynomials for the numerical solution of fractalâfractional model of nonlinear GinzburgâLandau equation
Mohammad Heydari, Abdon Atangana, Z. Avazzadeh
Engineering With Computers
Published: Nov 2019
30 citations
30 citations
415 days before retraction
Numerical solution of nonlinear 2D optimal control problems generated by Atangana-Riemann-Liouville fractal-fractional derivative
Mohammad Heydari
Applied Numerical Mathematics
Published: Nov 2019
46 citations
46 citations
443 days before retraction
An innovative optimal RPO-FOSMC based on multi-objective grasshopper optimization algorithm for DFIG-based wind turbine to augment MPPT and FRT capabilities
Ali Darvish Falehi
Chaos Solitons & Fractals
Published: Aug 2019
50 citations
50 citations
507 days before retraction
Chebyshev polynomials for generalized Couette flow of fractional Jeffrey nanofluid subjected to several thermochemical effects
Reza Roohi, Mohammad Heydari, Omid Bavi et al. (4 authors)
Engineering With Computers
Published: Aug 2019
51 citations
51 citations
523 days before retraction
Meshfree moving least squares method for nonlinear variable-order time fractional 2D telegraph equation involving MittagâLeffler non-singular kernel
M. Hosseininia, Mohammad Heydari
Chaos Solitons & Fractals
Published: Jul 2019
44 citations
44 citations
550 days before retraction
Legendre wavelets for the numerical solution of nonlinear variable-order time fractional 2D reaction-diffusion equation involving MittagâLeffler non-singular kernel
M. Hosseininia, Mohammad Heydari
Chaos Solitons & Fractals
Published: Jul 2019
37 citations
37 citations
550 days before retraction
RETRACTED ARTICLE: Research on influence model of fractional calculus derivative Fourier transform on aerobics view image reconstruction
Hao Liu, Wei Jiang, Anthony Lam
The European Physical Journal Plus
Published: Jul 2019
2 citations
2 citations
566 days before retraction
A new computing paradigm for the optimization of parameters in adaptive beamforming using fractional processing
Muhammad Asif Zahoor Raja, Rizwan Akhtar, Naveed Ishtiaq Chaudhary et al. (7 authors)
The European Physical Journal Plus
Published: Jun 2019
27 citations
27 citations
597 days before retraction
Exact solutions for the Atangana-Baleanu time-fractional model of a Brinkman-type nanofluid in a rotating frame: Applications in solar collectors
Aamina Aamina, Farhad Ali, Ilyas Khan et al. (5 authors)
The European Physical Journal Plus
Published: Mar 2019
10 citations
10 citations
689 days before retraction
A remark on the q-fractional order differential equations
Yongchao Tang, Tie Zhang
Applied Mathematics and Computation
Published: Jan 2019
27 citations
27 citations
731 days before retraction
Mathematical Modeling of Solutes Migration under the Conditions of Groundwater Filtration by the Model with the k-Caputo Fractional Derivative
Vsevolod Bohaienko, V. M. Bulavatsky
Fractal and Fractional
Open Access
Published: Oct 2018
5 citations
5 citations
817 days before retraction
Perturbation observer based fractional-order sliding-mode controller for MPPT of grid-connected PV inverters: Design and real-time implementation
Bo Yang, Tao Yu, Hongchun Shu et al. (7 authors)
Control Engineering Practice
Published: Jul 2018
91 citations
91 citations
904 days before retraction
Derivatives with Non-Singular Kernels from the Caputo-Fabrizio Definition and Beyond: Appraising Analysis with Emphasis on Diffusion Models
Jordan Hristov
Current developments in mathematical sciences
Published: Mar 2018
127 citations
127 citations
1036 days before retraction
Atangana-Batogna numerical scheme applied on a linear and non-linear fractional differential equation
Badr Saad T. Alkahtani
The European Physical Journal Plus
Published: Mar 2018
14 citations
14 citations
1054 days before retraction
Analysis of the cable equation with non-local and non-singular kernel fractional derivative
Berat KaraaÄaç
The European Physical Journal Plus
Published: Feb 2018
19 citations
19 citations
1082 days before retraction
Analytical and numerical solutions of the telegraph equation using the AtanganaâCaputo fractional order derivative
J.F. GĂłmezâAguilar
Journal of Electromagnetic Waves and Applications
Published: Nov 2017
9 citations
9 citations
1154 days before retraction
Analysis of the damped nonlinear space-fractional Schrödinger equation
Jiarui Liang, Songhe Song, Weien Zhou et al. (4 authors)
Applied Mathematics and Computation
Published: Nov 2017
6 citations
6 citations
1170 days before retraction
Numerical solution for highâorder linear complex differential equations with variable coefficients
Faruk DĂĆĂNCELÄ°, Ercan Ăelık
Numerical Methods for Partial Differential Equations
Published: Oct 2017
13 citations
13 citations
1193 days before retraction
Electrical circuits RC and RL involving fractional operators with bi-order
J.F. GĂłmezâAguilar, R.F. Escobar-JimĂ©nez, V. H. Olivares-Peregrino et al. (5 authors)
Advances in Mechanical Engineering
Open Access
Published: Jun 2017
21 citations
21 citations
1327 days before retraction
New solitary wave solutions to the (2+1)-dimensional CalogeroâBogoyavlenskiiâSchiff and the KadomtsevâPetviashvili hierarchy equations
Hacı Mehmet BaĆkonuĆ, Tukur Abdulkadir Sulaıman, Hasan Bulut
Indian Journal of Physics
Published: May 2017
55 citations
55 citations
1333 days before retraction
A new fractional operator of variable order: Application in the description of anomalous diffusion
XiaoâJun Yang, J. A. Tenreiro Machado
Physica A Statistical Mechanics and its Applications
Open Access
Published: Apr 2017
236 citations
236 citations
1370 days before retraction
Numerical solutions for solving time fractional FokkerâPlanck equations based on spectral collocation methods
Yin Yang, Yunqing Huang, Yong Zhou
Journal of Computational and Applied Mathematics
Published: Apr 2017
53 citations
53 citations
1377 days before retraction
Hyperchaotic behaviour obtained via a nonlocal operator with exponential decay and Mittag-Leffler laws
Abdon Atangana, J.F. GĂłmezâAguilar
Chaos Solitons & Fractals
Published: Mar 2017
88 citations
88 citations
1400 days before retraction
The Order of Convergence of Difference Schemes for Fractional Equations
Ru Liu, Miao Li, Sergey Piskarev
Numerical Functional Analysis and Optimization
Published: Mar 2017
7 citations
7 citations
1419 days before retraction
A novel cubature statistically linearized Kalman filter for fractional-order nonlinear discrete-time stochastic systems
Hamed Torabi, Naser Pariz, Ali Karimpour
Journal of Vibration and Control
Published: Feb 2017
7 citations
7 citations
1431 days before retraction
Fractional Hunter-Saxton equation involving partial operators with bi-order in Riemann-Liouville and Liouville-Caputo sense
J.F. GĂłmezâAguilar, Abdon Atangana
The European Physical Journal Plus
Published: Feb 2017
37 citations
37 citations
1447 days before retraction
The fractional Boussinesq equation of groundwater flow and its applications
Ninghu Su
Journal of Hydrology
Open Access
Published: Jan 2017
20 citations
20 citations
1466 days before retraction
Systems of semilinear evolution inequalities with temporal fractional derivative on the Heisenberg group
Meneceur Bekkar, Kamel Haouam, Amar Debbouche
Advances in Difference Equations
Open Access
Published: Jan 2017
4 citations
4 citations
1467 days before retraction
New insight in fractional differentiation: power, exponential decay and Mittag-Leffler laws and applications
J.F. GĂłmezâAguilar, Abdon Atangana
The European Physical Journal Plus
Published: Jan 2017
143 citations
143 citations
1478 days before retraction
Some Comprehensive Inequalities Consisting of Mittag-Leffler Type Functions in the Complex Plane
HĂŒseyiÌn Irmak, Praveen Agarwal
Mathematical Modelling of Natural Phenomena
Published: Jan 2017
8 citations
8 citations
1478 days before retraction
On Some Complex Aspects of the (2+1)-dimensional Broer-Kaup-Kupershmidt System
Hasan Bulut, Hilal Arslanoglu Isik, Tukur Abdulkadir Sulaıman
ITM Web of Conferences
Open Access
Published: Jan 2017
31 citations
31 citations
1478 days before retraction
Quick Stats
Total Citations:
48
Years Since Retraction:
4.8 years
Open Access:
Yes
Last Checked:
Jul 24, 2025