A different approach to the European option pricing model with new fractional operator
Math. Model. Nat. Phenom., 13 1 (2018) 12
Published online: 2018-04-06
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
A General Conformable Black–Scholes Equation for Option Pricing
Paula Morales-Bañuelos, Sebastian Elias Rodríguez Bojalil, Luis Alberto Quezada-Téllez and Guillermo Fernández-AnayaMathematics 13 (10) 1576 (2025)
https://doi.org/10.3390/math13101576
Fractional Insights in Tumor Modeling: An Interactive Study Between Tumor Carcinogenesis and Macrophage Activation
Parvaiz Ahmad Naik, Bijal M Yeolekar, Sania Qureshi, Mehmet Yavuz, Zhengxin Huang and Mahesh YeolekarAdvanced Theory and Simulations (2025)
https://doi.org/10.1002/adts.202401477
Qualitative financial modelling in fractal dimensions
Rami Ahmad El-Nabulsi and Waranont AnukoolFinancial Innovation 11 (1) (2025)
https://doi.org/10.1186/s40854-024-00723-2
Analysis and dynamics of the Ivancevic option pricing model with a novel fractional calculus approach
P. Veeresha and Devendra KumarWaves in Random and Complex Media 35 (3) 5376 (2025)
https://doi.org/10.1080/17455030.2022.2070684
Review of the Fractional Black-Scholes Equations and Their Solution Techniques
Hongmei Zhang, Mengchen Zhang, Fawang Liu and Ming ShenFractal and Fractional 8 (2) 101 (2024)
https://doi.org/10.3390/fractalfract8020101
Numerical analysis of fractional order Black–Scholes option pricing model with band equation method
Jiahao Chen, Xiaofei Li and Yunze ShaoJournal of Computational and Applied Mathematics 451 115998 (2024)
https://doi.org/10.1016/j.cam.2024.115998
Modeling and analysis of the fractional-order epidemic model to investigate mutual influence in HIV/HCV co-infection
Parvaiz Ahmad Naik, Bijal M. Yeolekar, Sania Qureshi, Mahesh Yeolekar and Anotida MadzvamuseNonlinear Dynamics 112 (13) 11679 (2024)
https://doi.org/10.1007/s11071-024-09653-1
Analyzing fractional effects on solutions of the generalized perturbed Zakharov-Kuznetsov equation using a residual series method with Caputo derivatives
Laiq Zada, Nasir Ali, Wasim Jamshed, Amjad Iqbal, Syed M. Hussain and Hijaz AhmadInternational Journal of Modelling and Simulation 1 (2024)
https://doi.org/10.1080/02286203.2024.2343171
High Order Numerical Scheme for Generalized Fractional Diffusion Equations
Kamlesh Kumar, A. K. Pandey and Rajesh K. PandeyInternational Journal of Applied and Computational Mathematics 10 (3) (2024)
https://doi.org/10.1007/s40819-024-01725-5
A study on the fractional Black–Scholes option pricing model of the financial market via the Yang-Abdel-Aty-Cattani operator
Surath GhoshEngineering Computations 41 (3) 611 (2024)
https://doi.org/10.1108/EC-08-2023-0452
Using a Mix of Finite Difference Methods and Fractional Differential Transformations to Solve Modified Black–Scholes Fractional Equations
Agus Sugandha, Endang Rusyaman, Sukono and Ema CarniaMathematics 12 (7) 1077 (2024)
https://doi.org/10.3390/math12071077
A comparative analytical investigation for some linear and nonlinear time-fractional partial differential equations in the framework of the Aboodh transformation
Saima Noor, Wedad Albalawi, Rasool Shah, Ahmad Shafee, Sherif M. E. Ismaeel and S. A. El-TantawyFrontiers in Physics 12 (2024)
https://doi.org/10.3389/fphy.2024.1374049
Solving Nonlinear Multi-Order Fractional Differential Equations Using Bernstein Polynomials
Shahad Adil Taher Algazaa and Jamshid SaeidianIEEE Access 11 128032 (2023)
https://doi.org/10.1109/ACCESS.2023.3332665
Fractional view of heat‐like equations via the Elzaki transform in the settings of the Mittag–Leffler function
Saima Rashid, Khadija Tul Kubra and Khadijah M. AbualnajaMathematical Methods in the Applied Sciences 46 (10) 11420 (2023)
https://doi.org/10.1002/mma.7793
Comparative Analysis of the Time-Fractional Black–Scholes Option Pricing Equations (BSOPE) by the Laplace Residual Power Series Method (LRPSM)
Muhammad Imran Liaqat, Eric Okyere and Watcharaporn CholamjiakJournal of Mathematics 2023 1 (2023)
https://doi.org/10.1155/2023/6092283
Study on fuzzy fractional European option pricing model with Mittag-Leffler kernel
Hebatollah Hashemi, Reza Ezzati, Naser Mikaeilvand and Mojtaba NazariJournal of Intelligent & Fuzzy Systems 45 (5) 8567 (2023)
https://doi.org/10.3233/JIFS-232094
Analytical Investigation of Some Time-Fractional Black–Scholes Models by the Aboodh Residual Power Series Method
Muhammad Imran Liaqat, Ali Akgül and Hanaa Abu-ZinadahMathematics 11 (2) 276 (2023)
https://doi.org/10.3390/math11020276
The modified homotopy perturbation method and its application to the dynamics of price evolution in Caputo-fractional order Black Scholes model
Adedapo Ismaila Alaje, Morufu Oyedunsi Olayiwola, Kamilu Adewale Adedokun, Joseph Adeleke Adedeji, Asimiyu Olamilekan Oladapo and Yunus Olanrewaju AkeemBeni-Suef University Journal of Basic and Applied Sciences 12 (1) (2023)
https://doi.org/10.1186/s43088-023-00433-1
Efficient Solution of Fractional-Order SIR Epidemic Model of Childhood Diseases With Optimal Homotopy Asymptotic Method
Okundalaye Oluwaseun Olumide, Wan Ainun Mior Othman and Necati OzdemirIEEE Access 10 9395 (2022)
https://doi.org/10.1109/ACCESS.2022.3141707
A Modified Black-Scholes-Merton Model for Option Pricing
Paula Morales-Bañuelos, Nelson Muriel and Guillermo Fernández-AnayaMathematics 10 (9) 1492 (2022)
https://doi.org/10.3390/math10091492
An Efficient Method for Solving Fractional Black-Scholes Model with Index and Exponential Decay Kernels
Saima Rashid, Saad Ihsan Butt, Zakia Hammouch, Ebenezer Bonyah and Alexander MeskhiJournal of Function Spaces 2022 1 (2022)
https://doi.org/10.1155/2022/2613133
Taming Hyperchaos with Exact Spectral Derivative Discretization Finite Difference Discretization of a Conformable Fractional Derivative Financial System with Market Confidence and Ethics Risk
Dominic P. Clemence-Mkhope and Gregory A. GibsonMathematical and Computational Applications 27 (1) 4 (2022)
https://doi.org/10.3390/mca27010004
Spectral Solutions for Fractional Black–Scholes Equations
M. A. Abdelkawy, António M. Lopes and Taseer MuhammadMathematical Problems in Engineering 2022 1 (2022)
https://doi.org/10.1155/2022/9365292
Numerical Solution of Time Fractional Black–Scholes Model Based on Legendre Wavelet Neural Network with Extreme Learning Machine
Xiaoning Zhang, Jianhui Yang and Yuxin ZhaoFractal and Fractional 6 (7) 401 (2022)
https://doi.org/10.3390/fractalfract6070401
Approximate Analytical Solution of Two-Dimensional Nonlinear Time-Fractional Damped Wave Equation in the Caputo Fractional Derivative Operator
Alemayehu Tamirie Deresse, Yesuf Obsie Mussa, Ademe Kebede Gizaw and José Francisco Gómez AguilarMathematical Problems in Engineering 2022 1 (2022)
https://doi.org/10.1155/2022/7004412
A Robust Analytical Method for Regularized Long Wave Equations
Haresh P. Jani and Twinkle R. SinghIranian Journal of Science and Technology, Transactions A: Science 46 (6) 1667 (2022)
https://doi.org/10.1007/s40995-022-01380-9
Numerical solving of generalized Black-Scholes differential equation using deep learning based on blocked residual connection
Muzhou Hou, Huawei Fu, Zheng Hu, et al.Digital Signal Processing 126 103498 (2022)
https://doi.org/10.1016/j.dsp.2022.103498
Caputo fractional-order SEIRP model for COVID-19 Pandemic
Saheed O. Akindeinde, Eric Okyere, Adebayo O. Adewumi, et al.Alexandria Engineering Journal 61 (1) 829 (2022)
https://doi.org/10.1016/j.aej.2021.04.097
Numerical Simulation of Elastic Wave Field in Viscoelastic Two-Phasic Porous Materials Based on Constant Q Fractional-Order BISQ Model
Ning Hu, Maofa Wang, Baochun Qiu and Yuanhong TaoMaterials 15 (3) 1020 (2022)
https://doi.org/10.3390/ma15031020
A New Homotopy Transformation Method for Solving the Fuzzy Fractional Black–Scholes European Option Pricing Equations under the Concept of Granular Differentiability
Jianke Zhang, Yueyue Wang and Sumei ZhangFractal and Fractional 6 (6) 286 (2022)
https://doi.org/10.3390/fractalfract6060286
Tangent nonlinear equation in context of fractal fractional operators with nonsingular kernel
Zain Ul Abadin Zafar, Ndolane Sene, Hadi Rezazadeh and Nafiseh EsfandianMathematical Sciences 16 (2) 121 (2022)
https://doi.org/10.1007/s40096-021-00403-7
New Illustrative Applications of Integral Transforms to Financial Models with Different Fractional Derivatives
Esra Karatas Akgül, Ali Akgül and Mehmet YavuzChaos, Solitons & Fractals 146 110877 (2021)
https://doi.org/10.1016/j.chaos.2021.110877
Numerical solving of the generalized Black-Scholes differential equation using Laguerre neural network
Yinghao Chen, Hanyu Yu, Xiangyu Meng, Xiaoliang Xie, Muzhou Hou and Julien ChevallierDigital Signal Processing 112 103003 (2021)
https://doi.org/10.1016/j.dsp.2021.103003
Analysis of an Electrical Circuit Using Two-Parameter Conformable Operator in the Caputo Sense
Ewa Piotrowska and Łukasz SajewskiSymmetry 13 (5) 771 (2021)
https://doi.org/10.3390/sym13050771
A Novel Homotopy Perturbation Algorithm Using Laplace Transform for Conformable Partial Differential Equations
Sajad Iqbal, Mohammed K. A. Kaabar, Francisco Martínez and Muhammad Shoaib AnwarMathematical Problems in Engineering 2021 1 (2021)
https://doi.org/10.1155/2021/2573067
A Novel Homotopy Perturbation Method with Applications to Nonlinear Fractional Order KdV and Burger Equation with Exponential-Decay Kernel
Shabir Ahmad, Aman Ullah, Ali Akgül, Manuel De la Sen and Alexander MeskhiJournal of Function Spaces 2021 1 (2021)
https://doi.org/10.1155/2021/8770488
Analytical solutions of some nonlinear fractional‐order differential equations by different methods
Meryem Odabasi, Zehra Pinar and Huseyin KocakMathematical Methods in the Applied Sciences 44 (9) 7526 (2021)
https://doi.org/10.1002/mma.6313
Novel comparison of numerical and analytical methods for fractional Burger–Fisher equation
Asif Yokus and Mehmet YavuzDiscrete & Continuous Dynamical Systems - S 14 (7) 2591 (2021)
https://doi.org/10.3934/dcdss.2020258
The Fractional View Analysis of Polytropic Gas, Unsteady Flow System
Hassan Khan, Saeed Islam, Muhammad Arif and Lishan LiuMathematical Problems in Engineering 2021 1 (2021)
https://doi.org/10.1155/2021/5130136
On Comparative Analysis for the Black-Scholes Model in the Generalized Fractional Derivatives Sense via Jafari Transform
Saima Rashid, Sobia Sultana, Rehana Ashraf, Mohammed K. A. Kaabar and Youssri Hassan YoussriJournal of Function Spaces 2021 1 (2021)
https://doi.org/10.1155/2021/7767848
Solving fractional Black–Scholes equation by using Boubaker functions
A.A. Khajehnasiri and M. SafaviMathematical Methods in the Applied Sciences 44 (11) 8505 (2021)
https://doi.org/10.1002/mma.7270
Application of the Generalized Laplace Homotopy Perturbation Method to the Time-Fractional Black–Scholes Equations Based on the Katugampola Fractional Derivative in Caputo Type
Sirunya Thanompolkrang, Wannika Sawangtong and Panumart SawangtongComputation 9 (3) 33 (2021)
https://doi.org/10.3390/computation9030033
Approximate-Analytical solution to the information measure’s based quanto option pricing model
Luckshay Batra and H.C. TanejaChaos, Solitons & Fractals 153 111493 (2021)
https://doi.org/10.1016/j.chaos.2021.111493
Fundamental calculus of the fractional derivative defined with Rabotnov exponential kernel and application to nonlinear dispersive wave model
Mehmet Yavuz and Ndolane SeneJournal of Ocean Engineering and Science 6 (2) 196 (2021)
https://doi.org/10.1016/j.joes.2020.10.004
Applications of Wavelet Multiresolution Analysis
Marcela A. Fabio, Silvia A. Seminara and María Inés TroparevskySEMA SIMAI Springer Series, Applications of Wavelet Multiresolution Analysis 4 1 (2021)
https://doi.org/10.1007/978-3-030-61713-4_1
Analytical and numerical approaches to nerve impulse model of fractional‐order
Mehmet Yavuz and Asıf YokusNumerical Methods for Partial Differential Equations 36 (6) 1348 (2020)
https://doi.org/10.1002/num.22476
Stability Analysis and Numerical Computation of the Fractional Predator–Prey Model with the Harvesting Rate
Mehmet Yavuz and Ndolane SeneFractal and Fractional 4 (3) 35 (2020)
https://doi.org/10.3390/fractalfract4030035
Fractional economic models based on market equilibrium in the frame of different type kernels
Bahar Acay, Erdal Bas and Thabet AbdeljawadChaos, Solitons & Fractals 130 109438 (2020)
https://doi.org/10.1016/j.chaos.2019.109438
European option pricing models described by fractional operators with classical and generalizedMittag‐Lefflerkernels
Mehmet YavuzNumerical Methods for Partial Differential Equations (2020)
https://doi.org/10.1002/num.22645
Modeling and analysis of COVID-19 epidemics with treatment in fractional derivatives using real data from Pakistan
Parvaiz Ahmad Naik, Mehmet Yavuz, Sania Qureshi, Jian Zu and Stuart TownleyThe European Physical Journal Plus 135 (10) (2020)
https://doi.org/10.1140/epjp/s13360-020-00819-5
A novel analytical technique for the solution of time-fractional Ivancevic option pricing model
Rajarama Mohan Jena, Snehashish Chakraverty and Dumitru BaleanuPhysica A: Statistical Mechanics and its Applications 550 124380 (2020)
https://doi.org/10.1016/j.physa.2020.124380
New collocation scheme for solving fractional partial differential equations
Chang PHANG, Afshan KANWAL and Jian Rong LOHHacettepe Journal of Mathematics and Statistics 49 (3) 1107 (2020)
https://doi.org/10.15672/hujms.459621
Solving Black–Scholes equations using fractional generalized homotopy analysis method
S. R. Saratha, G. Sai Sundara Krishnan, M. Bagyalakshmi and Chee Peng LimComputational and Applied Mathematics 39 (4) (2020)
https://doi.org/10.1007/s40314-020-01306-4
Novel Approaches for Getting the Solution of the Fractional Black–Scholes Equation Described by Mittag-Leffler Fractional Derivative
Ndolane Sene, Babacar Sène, Seydou Nourou Ndiaye and Awa TraoréDiscrete Dynamics in Nature and Society 2020 1 (2020)
https://doi.org/10.1155/2020/8047347
The role of prostitution on HIV transmission with memory: A modeling approach
Parvaiz Ahmad Naik, Mehmet Yavuz and Jian ZuAlexandria Engineering Journal 59 (4) 2513 (2020)
https://doi.org/10.1016/j.aej.2020.04.016
Fractional order oxygen–plankton system under climate change
Ramazan Ozarslan and Yadigar SekerciChaos: An Interdisciplinary Journal of Nonlinear Science 30 (3) (2020)
https://doi.org/10.1063/1.5129766
Nonlinear regularized long-wave models with a new integral transformation applied to the fractional derivative with power and Mittag-Leffler kernel
Mehmet Yavuz and Thabet AbdeljawadAdvances in Difference Equations 2020 (1) (2020)
https://doi.org/10.1186/s13662-020-02828-1
Model of economic growth in the context of fractional derivative
Awa Traore and Ndolane SeneAlexandria Engineering Journal 59 (6) 4843 (2020)
https://doi.org/10.1016/j.aej.2020.08.047
Chaotic dynamics of a fractional order HIV-1 model involving AIDS-related cancer cells
Parvaiz Ahmad Naik, Kolade M. Owolabi, Mehmet Yavuz and Jian ZuChaos, Solitons & Fractals 140 110272 (2020)
https://doi.org/10.1016/j.chaos.2020.110272
Complex conformable derivative
Sümeyra Uçar, Nihal Yılmaz Özgür and Beyza Billur İskender EroğluArabian Journal of Geosciences 12 (6) (2019)
https://doi.org/10.1007/s12517-019-4396-y
A Continuous Time Bertrand Duopoly Game With Fractional Delay and Conformable Derivative: Modeling, Discretization Process, Hopf Bifurcation, and Chaos
Baogui Xin, Wei Peng and Luca GuerriniFrontiers in Physics 7 (2019)
https://doi.org/10.3389/fphy.2019.00084
A new iterative method based solution for fractional Black–Scholes option pricing equations (BSOPE)
Rajarama Mohan Jena and S. ChakravertySN Applied Sciences 1 (1) (2019)
https://doi.org/10.1007/s42452-018-0106-8
Local generalization of transversality conditions for optimal control problem
Beyza Billur İskender Eroglu, Dіlara Yapişkan, D. Kumar, et al.Mathematical Modelling of Natural Phenomena 14 (3) 310 (2019)
https://doi.org/10.1051/mmnp/2019013
Black–Scholes option pricing equations described by the Caputo generalized fractional derivative
Aliou Niang Fall, Seydou Nourou Ndiaye and Ndolane SeneChaos, Solitons & Fractals 125 108 (2019)
https://doi.org/10.1016/j.chaos.2019.05.024
An efficient analytical approach for fractional equal width equations describing hydro-magnetic waves in cold plasma
Amit Goswami, Jagdev Singh, Devendra Kumar and SushilaPhysica A: Statistical Mechanics and its Applications 524 563 (2019)
https://doi.org/10.1016/j.physa.2019.04.058
Modeling, discretization, and hyperchaos detection of conformable derivative approach to a financial system with market confidence and ethics risk
Baogui Xin, Wei Peng, Yekyung Kwon and Yanqin LiuAdvances in Difference Equations 2019 (1) (2019)
https://doi.org/10.1186/s13662-019-2074-8
Homotopy Perturbation ρ-Laplace Transform Method and Its Application to the Fractional Diffusion Equation and the Fractional Diffusion-Reaction Equation
Ndolane Sene and Aliou Niang FallFractal and Fractional 3 (2) 14 (2019)
https://doi.org/10.3390/fractalfract3020014
An efficient analytical technique for fractional partial differential equations occurring in ion acoustic waves in plasma
Amit Goswami, Jagdev Singh, Devendra Kumar, Sumit Gupta and SushilaJournal of Ocean Engineering and Science 4 (2) 85 (2019)
https://doi.org/10.1016/j.joes.2019.01.003
Fractional Mass-Spring-Damper System Described by Generalized Fractional Order Derivatives
Ndolane Sene and José Francisco Gómez AguilarFractal and Fractional 3 (3) 39 (2019)
https://doi.org/10.3390/fractalfract3030039
A reliable treatment of residual power series method for time-fractional Black–Scholes European option pricing equations
Ved Prakash Dubey, Rajnesh Kumar and Devendra KumarPhysica A: Statistical Mechanics and its Applications 533 122040 (2019)
https://doi.org/10.1016/j.physa.2019.122040
Nonlocal Cauchy Problem via a Fractional Operator Involving Power Kernel in Banach Spaces
Ayşegül Keten, Mehmet Yavuz and Dumitru BaleanuFractal and Fractional 3 (2) 27 (2019)
https://doi.org/10.3390/fractalfract3020027
Homotopy methods for fractional linear/nonlinear differential equations with a local derivative operator
Mehmet YAVUZ and Burcu YAŞKIRANBalıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20 (3) 75 (2018)
https://doi.org/10.25092/baunfbed.476608
Applications of differential transformation method to solve systems of ordinary and partial differential equations
Ümit SARP, Fırat EVİRGEN and Sebahattin İKİKARDEŞBalıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20 (2) 135 (2018)
https://doi.org/10.25092/baunfbed.423145
Novel Recursive Approximation for Fractional Nonlinear Equations within Caputo-Fabrizio Operator
Mehmet Yavuz, C. Cattani, A. Atangana, et al.ITM Web of Conferences 22 01008 (2018)
https://doi.org/10.1051/itmconf/20182201008
An Alternative Approach for Nonlinear Optimization Problem with Caputo - Fabrizio Derivative
Fırat Evirgen, Mehmet Yavuz, C. Cattani, et al.ITM Web of Conferences 22 01009 (2018)
https://doi.org/10.1051/itmconf/20182201009
European Vanilla Option Pricing Model of Fractional Order without Singular Kernel
Mehmet Yavuz and Necati ÖzdemirFractal and Fractional 2 (1) 3 (2018)
https://doi.org/10.3390/fractalfract2010003
On the Solutions of Fractional Cauchy Problem Featuring Conformable Derivative
Mehmet Yavuz, Necati Özdemir, C. Cattani, et al.ITM Web of Conferences 22 01045 (2018)
https://doi.org/10.1051/itmconf/20182201045
Solutions of partial differential equations using the fractional operator involving Mittag-Leffler kernel
Mehmet Yavuz, Necati Ozdemir and Haci Mehmet BaskonusThe European Physical Journal Plus 133 (6) (2018)
https://doi.org/10.1140/epjp/i2018-12051-9