Papers

They are sorted chronically according to the field their are concerned with. If you would like to read any of my manuscripts please feel free to contact me.

Review papers

  • The Bushell-Okrasiński inequality, Mathematica Applicanda 50(1) (2022), 3-22, Journal

Anomalous diffusion: analytical and numerical approaches

  • Fractional material derivative: pointwise representation and a finite volume numerical scheme (with M. Teuerle), arXiv
  • Time-fractional porous medium equation: Erdélyi-Kober integral equations, compactly supported solutions, and numerical methods (with B. Lopez, J. Rocha, and H. Okrasińska-Płociniczak), Communications in Nonlinear Science and Numerical Simulation 128 (2024), 107692, www
  • Error of the Galerkin scheme for a semilinear subdiffusion equation with time-dependent coefficients and nonsmooth data, Computers & Mathematics with Applications Volume 127 (2022),181-191, Journal
  • Numerical scheme for Erdélyi–Kober fractional diffusion equation using Galerkin–Hermite method (with M. Świtała), Fractional Calculus and Applied Analysis 25, 1651–1687 (2022), arXiv, Journal
  • On a discrete composition of the fractional integral and Caputo derivative, Communications in Nonlinear Science and Numerical Simulation 108 (2022), 106234, arXiv, Journal
  • A linear Galerkin numerical method for a quasilinear subdiffusion equation, Applied Numerical Mathematics 185 (2023), 203-220, Journal, arXiv
  • Second order scheme for self-similar solutions of a time-fractional porous medium equation on the half-line, Applied Mathematics and Computation 424C (2022) 127033, arXiv, Journal
  • A weighted finite difference method for subdiffusive Black–Scholes model (with G.Krzyżanowski and M. Magdziarz), Computers & Mathematics with Applications 80 (5) (2020), pp. 653-670, www
  • Derivation of the nonlocal pressure form of the fractional porous medium equation in the hydrological setting, Communications in Nonlinear Science and Numerical Simulation 76C (2019) 66-70, www
  • Compactly supported solution of the time-fractional porous medium equation on the half-line (with M. Świtała), in preparation
  • Numerical method for a time-fractional porous medium equation, SIAM Journal on Numerical Analysis, 57(2) (2019), 638–656, PDF, www
  • Existence and uniqueness results for a time-fractional nonlinear diffusion equation (with M. Świtała), Journal of Mathematical Analysis and Applications 462(2) (2018), 1425-1434, www
  • Numerical method for Volterra equation with a power-type nonlinearity, Applied Mathematics and Computation 337 (2018), 452-460, www
  • Numerical schemes for integro-differential equations with Erdelyi-Kober fractional operator (with Sz. Sobieszek), Numerical Algorithms 76(1) (2017), pp. 125-150, www,
  • Diffusivity identification in a nonlinear time-fractional diffusion equation, Fractional Calculus and Applied Analysis 19(4) (2016), pp. 883-866, www,
  • Analytical studies of a time-fractional porous medium equation. Derivation, approximation and applications, Communications in Nonlinear Science and Numerical Simulation 24 (1–3) (2015), 169-183 , www
  • Approximation of the Erdelyi-Kober fractional operator with application to the time-fractional porous medium equation, SIAM Journal on Applied Mathematics 74(4) (2014), 1219–1237, PDF, www
  • Eigenvalue asymptotics of a fractional boundary-value problem, Applied Mathematics and Computation 241 (2014), 125-128, www
  • Approximate self-similar solutions to a nonlinear diffusion equation with time-fractional derivative (with H.Okrasińska), Physica D 261 (2013), 85-91, www
  • A note on fractional Bessel function and its asymptotics (with W.Okrasiński), Fractional Calculus and Applied Analysis 16 (3) (2013), 559-572, www
  • On asymptotics of some fractional differential equations, Mathematical Modelling and Analysis 18 (3) (2013), 358-373, www

Climate dynamics

  • Linear Galerkin-Legendre spectral scheme for a degenerate nonlinear and nonlocal parabolic equation arising in climatology, Applied Numerical Mathematics 179 (2022), 105-124, arXiv, Journal
  • Hopf bifurcation in a conceptual climate model with ice-albedo and precipitation-temperature feedbacks, Nonlinear Analysis: Real World Applications 51 (2020), 102967, www
  • Asymptotic analysis of internal relaxation-oscillations in a conceptual climate model, IMA Journal of Applied Mathematics 85 (3) (2020), 467–494, www

Capillary phenomena

  • Oscillatory behaviour analysis of a liquid rise in cylindrical capillaries (with M. Świtała), Communications in Nonlinear Science and Numerical Simulations 96 (2021), 105647www
  • Asymptotic behaviour of a solution to a nonlinear equation modelling capillary rise (with M. Świtała), Physica D 406 (2020), 132394, www
  • Solvability in Hölder spaces of an integral equation which models dynamics of the capillary rise (with K. Sadarangani, J. Rocha and H.Okrasińska-Płociniczak), Journal of Mathematical Analysis and Applications 490(1) (2020), 124237, www
  • Monotonicity, oscillations and stability of a solution to a nonlinear equation modelling the capillary rise (with M. Świtała), Physica D 362 (2018), pp. 1-8, www

Mathematics of sports

  • Optimal strategy for trail running with nutrition and fatigue factors (with B. Jaszczak), www
  • Stability of fixed points in an approximate solution of the spring-mass running model (with P. Kowalczyk and Z. Wróblewska), IMA Journal of Applied Mathematics 88 (3) (2023), 429–454, www.
  • Energy variations and periodic solutions in a switched inverted pendulum model of human running gaits (with P. Kowalczyk and Z. Wróblewska), Physica D 443 (2023), 133554, Journal
  • Asymptotic solution of a boundary value problem for a spring-mass model of legged locomotion, Journal of Nonlinear Science 30, 2971–2988(2020), www.
  • Solution and asymptotic analysis of a boundary value problem in the spring-mass model of running (with. Z. Wróblewska), Nonlinear Dynamics 99 (2020), 2693–2705, www

Corneal topography

  • Solution estimates for a system of nonlinear integral equations arising in optometry (with W. Okrasiński), Journal of Integral Equations and Applications 30(1) (2018), pp. 167-179
  • Analysis of cornea curvature using radial basis functions - Part I: Methodology (with G. Griffiths and W. Schiesser), Computers in Biology and Medicine, 77 (2016), pp. 274-284, www
  • Analysis of cornea curvature using radial basis functions - Part II: Fitting to data-set (with G. Griffiths and W. Schiesser), Computers in Biology and Medicine 77 (2016), pp. 285-296, www
  • ODE/PDE Analysis of Corneal Curvature (with W.E.Schiesser and G.W.Griffiths), Computers in Biology and Medicine 53 (2014), 30-41, www
  • Nonliear Parameter Identification in Corneal Geometry Model (with W.Okrasiński), Inverse Problems in Science and Engineering 23 (3) (2015), 443-456, www
  • On a nonlinear boundary value problem modeling corneal shape (with W.Okrasiński, J.J.Nieto and O.Dominguez), Journal of Mathematical Analysis and Applications 414 (1) (2014), 461–471, www
  • Bessel function model of corneal topography (with W.Okrasiński), Applied Mathematics and Computation 223 (2013), 436-443, www
  • Regularization of an Ill-posed Problem in Corneal Topography (with W.Okrasiński), Inverse Problems in Science and Engineering 21 (6) (2013), 1090–1097, www
  • A Nonlinear Mathematical Model of the Corneal Shape (with W.Okrasiński), Nonlinear Analysis: Real World Applications 13 (2012), 1498-1505, www

Miscellaneous

  • The Bushell-Okrasiński inequality, www
  • Mathematician makes wine. PART I: Wine and juice analysis (with M. Skarupski), in preparation
  • Off-axis vortex beam propagation through classical optical system in terms of Kummer confluent hypergeometric function (with I. Augustyniak, W. Lamperska, J. Masajada and A. Popiołek-Masajada), Photonics 7(3) (2020), 60.
  • Quickest drift change detection in Lévy-type force of mortality model (with M. Krawiec and Z. Palmowski), Applied Mathematics and Computation 338 (2018), pp. 432-450, www
  • Regularization and the inflection point method for a sensor signal in gas concentration measurement (with M. Maciejewska and A. Szczurek), Inverse Problems in Science and Engineering 25(4) (2017), pp. 555-579, www
  • Transformation of the vortex beam in the optical vortex scanning microscope (with A. Popiołek-Masajada, M. Szatkowski and D. Wojnowski), Optics & Laser Technology 81 (2016), pp. 127–136, www
  • Analytical model of the optical vortex microscope (with A. Popiołek-Masajada, J. Masajada and M. Szatkowski), Applied Optics 55(12) (2016), pp. B20-B27, www
  • High order vortex beam in the optical vortex microscope (with A. Popiołek-Masajada, M. Szatkowski and J. Masajada), SPIE Optical Engineering+ Applications, International Society for Optics and Photonics (2015) p. 95810N-95810N-8, www

Some Conference Presentations and Lectures

In Polish:

Other works

  • P.Malinowski, M.Muszkieta, Ł.Płociniczak, M.Teuerle, Metoda statystyczna wyboru budynków do przeprowadzenia eksperymentu pomiarowego, rozdział w Nowoczesne rozwiązania w inżynierii i ochronie środowiska, Tom II, Oficyna Wydawnicza PWr, Wrocław, 2011
  • A.Fitt, M.Frąszczak, Ł.Płociniczak, M.Przybyłko, J.Orewczyk, P.Urbaniec, M. Wielgus, Determinig Intraocular Pressure in a Noninvasive Way, EMS School On Mathematical Modeling, Będlewo, 2010
  • M.Bracke, O.Corradi, J.P.Frexia, Ł.Płociniczak, P.Trinh, J.Ufitimana, M Yudistkiy, Thermal Conduction In Beehives, 23rd Modeling Week, Wrocław, 2009
  • Ł.Płociniczak, Mathematical Models of Corneal Topography, Master Thesis, PWr, Wrocław, 2011
  • Ł.Płociniczak, Mathematical Analysis of a New Conreal Topography Model, PhD Thesis, PWr, Wrocław, 2012