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.

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

• 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

• 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

• 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

• Discussion on angular asymmetry in the solutions of SLIP model (with z P. Kowalczyki i Z. Wróblewska), Mathematica Applicanda 51(2) (2023), 233–237 www
• 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

• 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

• 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

• Applied Mathematics and Mathematical Methods in Physics, Gdańsk, 2013, Anomalous diffusion
• Between Theory and Applications - Mathematics in Action, Będlewo, 2013, Mathematics of human eye
• ESGI 103 PhD Course Modern Methods in Industrial Mathematics, Technical University of Denmark, 2014, Applications of the fractional calculus, Problem set

In Polish:

• Kobyla Góra, 2014, Wszechświat w 30min (popularne wprowadzenie do kosmologii)
• Kobyla Góra, 2014, O matematyce na opak (krótko o problemach odwrotnych)

• 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