Mathematical Modelling of Natural Phenomena

Дробове рiвняння дифузiї, що вироджується на початковiй гiперплощинi.

A. M. Ponomarenko
Ukrains’kyi Matematychnyi Zhurnal 73 (3) 370 (2021)
DOI: 10.37863/umzh.v73i3.6320
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Time-Non-Local Pearson Diffusions

Giacomo Ascione, Nikolai Leonenko and Enrica Pirozzi
Journal of Statistical Physics 183 (3) (2021)
DOI: 10.1007/s10955-021-02786-2
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Finite dimensional Fokker–Planck equations for continuous time random walk limits

Ofer Busani
Stochastic Processes and their Applications 127 (5) 1496 (2017)
DOI: 10.1016/j.spa.2016.08.008
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Intermittence and Space-Time Fractional Stochastic Partial Differential Equations

Jebessa B. Mijena and Erkan Nane
Potential Analysis 44 (2) 295 (2016)
DOI: 10.1007/s11118-015-9512-3
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Correlation structure of fractional Pearson diffusions

Nikolai N. Leonenko, Mark M. Meerschaert and Alla Sikorskii
Computers & Mathematics with Applications 66 (5) 737 (2013)
DOI: 10.1016/j.camwa.2013.01.009
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Convoluted fractional Poisson process of order k

Ayushi S. Sengar and Neelesh S. Upadhye
Stochastics 1 (2023)
DOI: 10.1080/17442508.2023.2165399
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On fractional tempered stable processes and their governing differential equations

Luisa Beghin
Journal of Computational Physics 293 29 (2015)
DOI: 10.1016/j.jcp.2014.05.026
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Some Skew-Symmetric Distributions Which Include the Bimodal Ones

Dexter O. Cahoy
Communications in Statistics - Theory and Methods 44 (3) 554 (2015)
DOI: 10.1080/03610926.2012.746986
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Razumikhin-type theorem on time-changed stochastic functional differential equations with Markovian switching

Xiaozhi Zhang and Chenggui Yuan
Open Mathematics 17 (1) 689 (2019)
DOI: 10.1515/math-2019-0055
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Asymptotic degeneracy and subdiffusivity

Sida Yuan and Reiichiro Kawai
Journal of Physics A: Mathematical and Theoretical 53 (9) 095002 (2020)
DOI: 10.1088/1751-8121/ab69a5
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Path stability of stochastic differential equations driven by time-changed Lévy noises

Erkan Nane and Yinan Ni
Latin American Journal of Probability and Mathematical Statistics 15 (1) 479 (2018)
DOI: 10.30757/ALEA.v15-20
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Time-fractional geometric Brownian motion from continuous time random walks

C.N. Angstmann, B.I. Henry and A.V. McGann
Physica A: Statistical Mechanics and its Applications 526 121002 (2019)
DOI: 10.1016/j.physa.2019.04.238
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Tempered fractional Poisson processes and fractional equations with Z-transform

Neha Gupta, Arun Kumar and Nikolai Leonenko
Stochastic Analysis and Applications 38 (5) 939 (2020)
DOI: 10.1080/07362994.2020.1748056
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Non-Gaussian diffusion of mixed origins

Yann Lanoiselée and Denis S Grebenkov
Journal of Physics A: Mathematical and Theoretical 52 (30) 304001 (2019)
DOI: 10.1088/1751-8121/ab2826
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Moment-based estimation for parameters of general inverse subordinator

Aleksandra Grzesiek, Rafał Połoczański, Arun Kumar and Agnieszka Wyłomańska
Physica A: Statistical Mechanics and its Applications 575 126042 (2021)
DOI: 10.1016/j.physa.2021.126042
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Method of variable separation for investigating exact solutions and dynamical properties of the time-fractional Fokker–Planck equation

Weiguo Rui, Xinsong Yang and Fen Chen
Physica A: Statistical Mechanics and its Applications 595 127068 (2022)
DOI: 10.1016/j.physa.2022.127068
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Comb Model with Slow and Ultraslow Diffusion

T. Sandev, A. Iomin, H. Kantz, et al.
Mathematical Modelling of Natural Phenomena 11 (3) 18 (2016)
DOI: 10.1051/mmnp/201611302
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A Semi-Markov Algorithm for Continuous Time Random Walk Limit Distributions

G. Gill, P. Straka, A. Nepomnyashchy and V. Volpert
Mathematical Modelling of Natural Phenomena 11 (3) 34 (2016)
DOI: 10.1051/mmnp/201611303
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Giacomo Ascione, Nikolai Leonenko and Enrica Pirozzi
26 1 (2021)
DOI: 10.1007/978-3-030-69236-0_1
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Aditya Maheshwari and Reetendra Singh
26 205 (2021)
DOI: 10.1007/978-3-030-69236-0_11
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A Hopf-Lax formula for Hamilton-Jacobi equations with Caputo time-fractional derivative

Fabio Camilli, Raul De Maio and Elisa Iacomini
Journal of Mathematical Analysis and Applications 477 (2) 1019 (2019)
DOI: 10.1016/j.jmaa.2019.04.069
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Modeling transport through an environment crowded by a mixture of obstacles of different shapes and sizes

Adam J. Ellery, Ruth E. Baker, Scott W. McCue and Matthew J. Simpson
Physica A: Statistical Mechanics and its Applications 449 74 (2016)
DOI: 10.1016/j.physa.2015.12.123
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Convolution-Type Derivatives, Hitting-Times of Subordinators and Time-Changed C 0-semigroups

Bruno Toaldo
Potential Analysis 42 (1) 115 (2015)
DOI: 10.1007/s11118-014-9426-5
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Stochastic solutions for fractional wave equations

Mark M. Meerschaert, René L. Schilling and Alla Sikorskii
Nonlinear Dynamics 80 (4) 1685 (2015)
DOI: 10.1007/s11071-014-1299-z
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Renewal Theory for a System with Internal States

M. Niemann, E. Barkai, H. Kantz, A. Nepomnyashchy and V. Volpert
Mathematical Modelling of Natural Phenomena 11 (3) 191 (2016)
DOI: 10.1051/mmnp/201611312
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Time-Inhomogeneous Jump Processes and Variable Order Operators

Enzo Orsingher, Costantino Ricciuti and Bruno Toaldo
Potential Analysis 45 (3) 435 (2016)
DOI: 10.1007/s11118-016-9551-4
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Characterization of the inverse stable subordinator

Farouk Mselmi
Statistics & Probability Letters 140 37 (2018)
DOI: 10.1016/j.spl.2018.04.007
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BOUNDS ON THE SUPPORT OF THE MULTIFRACTAL SPECTRUM OF STOCHASTIC PROCESSES

DANIJEL GRAHOVAC and NIKOLAI N. LEONENKO
Fractals 26 (04) 1850055 (2018)
DOI: 10.1142/S0218348X1850055X
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Time dependent random fields on spherical non-homogeneous surfaces

Mirko D’Ovidio and Erkan Nane
Stochastic Processes and their Applications 124 (6) 2098 (2014)
DOI: 10.1016/j.spa.2014.02.001
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Fractional Calculus and Fractional Differential Equations

K. K. Kataria and P. Vellaisamy
Trends in Mathematics, Fractional Calculus and Fractional Differential Equations 17 (2019)
DOI: 10.1007/978-981-13-9227-6_2
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Anomalous diffusion with ballistic scaling: A new fractional derivative

James F. Kelly, Cheng-Gang Li and Mark M. Meerschaert
Journal of Computational and Applied Mathematics 339 161 (2018)
DOI: 10.1016/j.cam.2017.11.012
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Some Large Deviations Principles for Time-Changed Gaussian Processes

Barbara Pacchiarotti
Lithuanian Mathematical Journal 60 (4) 513 (2020)
DOI: 10.1007/s10986-020-09494-6
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Fractionally integrated inverse stable subordinators

Alexander Iksanov, Zakhar Kabluchko, Alexander Marynych and Georgiy Shevchenko
Stochastic Processes and their Applications 127 (1) 80 (2017)
DOI: 10.1016/j.spa.2016.06.001
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On the infinite divisibility of distributions of some inverse subordinators

Arun Kumar and Erkan Nane
Modern Stochastics: Theory and Applications 509 (2018)
DOI: 10.15559/18-VMSTA108
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Fractional Brownian Motion Delayed by Tempered and Inverse Tempered Stable Subordinators

A. Kumar, J. Gajda, A. Wyłomańska and R. Połoczański
Methodology and Computing in Applied Probability 21 (1) 185 (2019)
DOI: 10.1007/s11009-018-9648-x
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Fractional Equations and Models

Trifce Sandev and Živorad Tomovski
Developments in Mathematics, Fractional Equations and Models 61 115 (2019)
DOI: 10.1007/978-3-030-29614-8_4
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Fractional Queues with Catastrophes and Their Transient Behaviour

Giacomo Ascione, Nikolai Leonenko and Enrica Pirozzi
Mathematics 6 (9) 159 (2018)
DOI: 10.3390/math6090159
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Models for characterizing the transition among anomalous diffusions with different diffusion exponents

Trifce Sandev, Weihua Deng and Pengbo Xu
Journal of Physics A: Mathematical and Theoretical 51 (40) 405002 (2018)
DOI: 10.1088/1751-8121/aad8c9
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Space–time fractional stochastic partial differential equations

Jebessa B. Mijena and Erkan Nane
Stochastic Processes and their Applications 125 (9) 3301 (2015)
DOI: 10.1016/j.spa.2015.04.008
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Subordinated affine structure models for commodity future prices

M. Kateregga, S. Mataramvura, D. Taylor and Lanouar Charfeddine
Cogent Economics & Finance 6 (1) 1512360 (2018)
DOI: 10.1080/23322039.2018.1512360
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Solving Multidimensional Fractional Fokker--Planck Equations via Unbiased Density Formulas for Anomalous Diffusion Processes

Sean Carnaffan and Reiichiro Kawai
SIAM Journal on Scientific Computing 39 (5) B886 (2017)
DOI: 10.1137/17M111482X
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The fractional d'Alembert's formulas

Cheng-Gang Li, Miao Li, Sergey Piskarev and Mark M. Meerschaert
Journal of Functional Analysis 277 (12) 108279 (2019)
DOI: 10.1016/j.jfa.2019.108279
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Relaxation patterns and semi-Markov dynamics

Mark M. Meerschaert and Bruno Toaldo
Stochastic Processes and their Applications 129 (8) 2850 (2019)
DOI: 10.1016/j.spa.2018.08.004
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Non-homogeneous space-time fractional Poisson processes

A. Maheshwari and P. Vellaisamy
Stochastic Analysis and Applications 37 (2) 137 (2019)
DOI: 10.1080/07362994.2018.1541749
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Fractional immigration-death processes

Giacomo Ascione, Nikolai Leonenko and Enrica Pirozzi
Journal of Mathematical Analysis and Applications 495 (2) 124768 (2021)
DOI: 10.1016/j.jmaa.2020.124768
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Space-time duality and high-order fractional diffusion

James F. Kelly and Mark M. Meerschaert
Physical Review E 99 (2) (2019)
DOI: 10.1103/PhysRevE.99.022122
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A Semi-Markov Leaky Integrate-and-Fire Model

Giacomo Ascione and Bruno Toaldo
Mathematics 7 (11) 1022 (2019)
DOI: 10.3390/math7111022
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Inverse Stable Prior for Exponential Models

Dexter Cahoy and Joseph Sedransk
Journal of Statistical Theory and Practice 13 (2) (2019)
DOI: 10.1007/s42519-018-0027-2
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Aging uncoupled continuous time random walk limits

Ofer Busani
Electronic Journal of Probability 21 (none) (2016)
DOI: 10.1214/16-EJP3802
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The fractional non-homogeneous Poisson process

Nikolai Leonenko, Enrico Scalas and Mailan Trinh
Statistics & Probability Letters 120 147 (2017)
DOI: 10.1016/j.spl.2016.09.024
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Probabilistic representation formula for the solution of fractional high-order heat-type equations

Stefano Bonaccorsi, Mirko D’Ovidio and Sonia Mazzucchi
Journal of Evolution Equations 19 (2) 523 (2019)
DOI: 10.1007/s00028-019-00485-w
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Truncated Euler-Maruyama method for classical and time-changed non-autonomous stochastic differential equations

Wei Liu, Xuerong Mao, Jingwen Tang and Yue Wu
Applied Numerical Mathematics 153 66 (2020)
DOI: 10.1016/j.apnum.2020.02.007
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Random time-changes and asymptotic results for a class of continuous-time Markov chains on integers with alternating rates

Luisa Beghin, Claudio Macci and Barbara Martinucci
Modern Stochastics: Theory and Applications 1 (2020)
DOI: 10.15559/20-VMSTA169
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Weak error for Continuous Time Markov Chains related to fractional in time P(I)DEs

M. Kelbert, V. Konakov and S. Menozzi
Stochastic Processes and their Applications 126 (4) 1145 (2016)
DOI: 10.1016/j.spa.2015.10.013
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Computer Aided Systems Theory – EUROCAST 2019

Giacomo Ascione
Lecture Notes in Computer Science, Computer Aided Systems Theory – EUROCAST 2019 12013 220 (2020)
DOI: 10.1007/978-3-030-45093-9_27
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A fractional PDE for first passage time of time-changed Brownian motion and its numerical solution

M. Abundo, G. Ascione, M.F. Carfora and E. Pirozzi
Applied Numerical Mathematics 155 103 (2020)
DOI: 10.1016/j.apnum.2019.07.020
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Fractional Erlang queues

Giacomo Ascione, Nikolai Leonenko and Enrica Pirozzi
Stochastic Processes and their Applications 130 (6) 3249 (2020)
DOI: 10.1016/j.spa.2019.09.012
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Bismut–Elworthy–Li formula for subordinated Brownian motion applied to hedging financial derivatives

M. Kateregga, S. Mataramvura, D. Taylor and Xibin Zhang
Cogent Economics & Finance 5 (1) 1384125 (2017)
DOI: 10.1080/23322039.2017.1384125
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Applications of inverse tempered stable subordinators

Mahmoud S. Alrawashdeh, James F. Kelly, Mark M. Meerschaert and Hans-Peter Scheffler
Computers & Mathematics with Applications 73 (6) 892 (2017)
DOI: 10.1016/j.camwa.2016.07.026
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Relation between generalized diffusion equations and subordination schemes

A. Chechkin and I. M. Sokolov
Physical Review E 103 (3) (2021)
DOI: 10.1103/PhysRevE.103.032133
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Non-local Solvable Birth–Death Processes

Giacomo Ascione, Nikolai Leonenko and Enrica Pirozzi
Journal of Theoretical Probability 35 (2) 1284 (2022)
DOI: 10.1007/s10959-021-01087-4
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Intermittency fronts for space-time fractional stochastic partial differential equations in (d+1) dimensions

Sunday A. Asogwa and Erkan Nane
Stochastic Processes and their Applications 127 (4) 1354 (2017)
DOI: 10.1016/j.spa.2016.08.002
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A fractional multi-states model for insurance

Donatien Hainaut
Insurance: Mathematics and Economics 98 120 (2021)
DOI: 10.1016/j.insmatheco.2021.02.004
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Hadamard-Type Fractional Heat Equations and Ultra-Slow Diffusions

Alessandro De Gregorio and Roberto Garra
Fractal and Fractional 5 (2) 48 (2021)
DOI: 10.3390/fractalfract5020048
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Space‐time fractional Dirichlet problems

Boris Baeumer, Tomasz Luks and Mark M. Meerschaert
Mathematische Nachrichten 291 (17-18) 2516 (2018)
DOI: 10.1002/mana.201700111
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Carson Ingo, Richard L. Magin, Luis Colon-Perez and Thomas H. Mareci
1 (2014)
DOI: 10.1109/ICFDA.2014.6967418
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Limit theorems for the fractional nonhomogeneous Poisson process

Nikolai Leonenko, Enrico Scalas and Mailan Trinh
Journal of Applied Probability 56 (01) 246 (2019)
DOI: 10.1017/jpr.2019.16
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A Continuous-Time Random Walk Extension of the Gillis Model

Gaia Pozzoli, Mattia Radice, Manuele Onofri and Roberto Artuso
Entropy 22 (12) 1431 (2020)
DOI: 10.3390/e22121431
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Fractional Diffusion Equation Degenerating in the Initial Hyperplane

A. M. Ponomarenko
Ukrainian Mathematical Journal 73 (3) 433 (2021)
DOI: 10.1007/s11253-021-01934-x
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Asymmetric random walks with bias generated by discrete-time counting processes

Thomas M. Michelitsch, Federico Polito and Alejandro P. Riascos
Communications in Nonlinear Science and Numerical Simulation 109 106121 (2022)
DOI: 10.1016/j.cnsns.2021.106121
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Time-changed fractional Ornstein-Uhlenbeck process

Giacomo Ascione, Yuliya Mishura and Enrica Pirozzi
Fractional Calculus and Applied Analysis 23 (2) 450 (2020)
DOI: 10.1515/fca-2020-0022
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The Probabilistic Point of View on the Generalized Fractional Partial Differential Equations

Vassili N. Kolokoltsov
Fractional Calculus and Applied Analysis 22 (3) 543 (2019)
DOI: 10.1515/fca-2019-0033
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On a Fractional Stochastic Risk Model with a Random Initial Surplus and a Multi-Layer Strategy

Enrica Pirozzi
Mathematics 10 (4) 570 (2022)
DOI: 10.3390/math10040570
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Stochastic solutions for time-fractional heat equations with complex spatial variables

Luisa Beghin and Alessandro De Gregorio
Fractional Calculus and Applied Analysis 25 (1) 244 (2022)
DOI: 10.1007/s13540-021-00011-1
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Subordination and memory dependent kinetics in diffusion and relaxation phenomena

Katarzyna Górska and Andrzej Horzela
Fractional Calculus and Applied Analysis 26 (2) 480 (2023)
DOI: 10.1007/s13540-023-00141-8
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Continuity of the Solution to a Stochastic Time-fractional Diffusion Equations in the Spatial Domain with Locally Lipschitz Sources

Dang Duc Trong, Nguyen Dang Minh, Nguyen Nhu Lan and Nguyen Thi Mong Ngoc
Acta Mathematica Vietnamica 48 (1) 237 (2023)
DOI: 10.1007/s40306-023-00503-7
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Skorokhod Reflection Problem for Delayed Brownian Motion with Applications to Fractional Queues

Giacomo Ascione, Nikolai Leonenko and Enrica Pirozzi
Symmetry 14 (3) 615 (2022)
DOI: 10.3390/sym14030615
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Queuing models with Mittag-Leffler inter-event times

Jacob Butt, Nicos Georgiou and Enrico Scalas
Fractional Calculus and Applied Analysis (2023)
DOI: 10.1007/s13540-023-00161-4
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Tychonoff Solutions of the Time-Fractional Heat Equation

Giacomo Ascione
Fractal and Fractional 6 (6) 292 (2022)
DOI: 10.3390/fractalfract6060292
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An elementary proof for dynamical scaling for certain fractional non-homogeneous Poisson processes

Markus Kreer
Statistics & Probability Letters 182 109296 (2022)
DOI: 10.1016/j.spl.2021.109296
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First passage times for some classes of fractional time-changed diffusions

Nikolai Leonenko and Enrica Pirozzi
Stochastic Analysis and Applications 40 (4) 735 (2022)
DOI: 10.1080/07362994.2021.1953386
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On densities of the product, quotient and power of independent subordinators

K.K. Kataria and P. Vellaisamy
Journal of Mathematical Analysis and Applications 462 (2) 1627 (2018)
DOI: 10.1016/j.jmaa.2018.02.059
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Chernoff Approximation for Semigroups Generated by Killed Feller Processes and Feynman Formulae for Time-Fractional Fokker–Planck–Kolmogorov Equations

Yana A. Butko
Fractional Calculus and Applied Analysis 21 (5) 1203 (2018)
DOI: 10.1515/fca-2018-0065
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Asymptotics of Fundamental Solutions for Time Fractional Equations with Convolution Kernels

Yuri Kondratiev, Andrey Piatnitski and Elena Zhizhina
Fractional Calculus and Applied Analysis 23 (4) 1161 (2020)
DOI: 10.1515/fca-2020-0059
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Space-time fractional stochastic partial differential equations with Lévy noise

Xiangqian Meng and Erkan Nane
Fractional Calculus and Applied Analysis 23 (1) 224 (2020)
DOI: 10.1515/fca-2020-0009
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Non-linear Noise Excitation for some Space-Time Fractional Stochastic Equations in Bounded Domains

Mohammud Foondun, Jebessa B. Mijena and Erkan Nane
Fractional Calculus and Applied Analysis 19 (6) 1527 (2016)
DOI: 10.1515/fca-2016-0079
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On a fractional queueing model with catastrophes

Matheus de Oliveira Souza and Pablo M. Rodriguez
Applied Mathematics and Computation 410 126468 (2021)
DOI: 10.1016/j.amc.2021.126468
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The Fokker–Planck equation for the time-changed fractional Ornstein–Uhlenbeck stochastic process

Giacomo Ascione, Yuliya Mishura and Enrica Pirozzi
Proceedings of the Royal Society of Edinburgh: Section A Mathematics 152 (4) 1032 (2022)
DOI: 10.1017/prm.2021.45
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Skellam and time-changed variants of the generalized fractional counting process

Kuldeep Kumar Kataria and Mostafizar Khandakar
Fractional Calculus and Applied Analysis 25 (5) 1873 (2022)
DOI: 10.1007/s13540-022-00091-7
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Fractional Modeling in Action: a Survey of Nonlocal Models for Subsurface Transport, Turbulent Flows, and Anomalous Materials

Jorge L. Suzuki, Mamikon Gulian, Mohsen Zayernouri and Marta D’Elia
Journal of Peridynamics and Nonlocal Modeling (2022)
DOI: 10.1007/s42102-022-00085-2
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Level of noises and long time behavior of the solution for space-time fractional SPDE in bounded domains

Jebessa B. Mijena, Erkan Nane and Alemayehu G. Negash
Discrete and Continuous Dynamical Systems - S (2022)
DOI: 10.3934/dcdss.2022180
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Dynamical behavior of stochastic cellular neural networks with distributed time delays

Ling Zhang and Xiaoqi Sun
Mathematical Methods in the Applied Sciences 46 (5) 5850 (2023)
DOI: 10.1002/mma.8872
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Probabilistic solutions of fractional differential and partial differential equations and their Monte Carlo simulations

T. Oraby, E. Suazo and H. Arrubla
Chaos, Solitons & Fractals 166 112901 (2023)
DOI: 10.1016/j.chaos.2022.112901
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Nonlocal in-time telegraph equation and telegraph processes with random time

Francisco Alegría, Verónica Poblete and Juan C. Pozo
Journal of Differential Equations 347 310 (2023)
DOI: 10.1016/j.jde.2022.12.001
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