\\ ====== 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, [[https://wydawnictwa.ptm.org.pl/index.php/matematyka-stosowana/article/view/7130/6560|Journal]] ===== Anomalous diffusion: analytical and numerical approaches===== * **Fractional material derivative: pointwise representation and a finite volume numerical scheme** (with M. Teuerle), [[https://arxiv.org/abs/2402.19015|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, [[https://www.sciencedirect.com/science/article/pii/S1007570423006135?via%3Dihub|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, [[https://www.sciencedirect.com/science/article/pii/S089812212200414X|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), [[https://arxiv.org/pdf/2202.06156.pdf|arXiv]], [[https://link.springer.com/article/10.1007/s13540-022-00063-x|Journal]] * **On a discrete composition of the fractional integral and Caputo derivative**, Communications in Nonlinear Science and Numerical Simulation 108 (2022), 106234, [[https://arxiv.org/pdf/2107.10489v2.pdf|arXiv]], [[https://www.sciencedirect.com/science/article/pii/S1007570421004913|Journal]] * **A linear Galerkin numerical method for a quasilinear subdiffusion equation**, Applied Numerical Mathematics 185 (2023), 203-220, [[https://www.sciencedirect.com/science/article/pii/S0168927422003075?dgcid=author|Journal]], [[https://arxiv.org/abs/2107.10057|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, [[https://arxiv.org/pdf/2106.05138|arXiv]], [[https://www.sciencedirect.com/science/article/abs/pii/S0096300322001199|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, [[https://www.sciencedirect.com/science/article/pii/S0898122120301760?dgcid=coauthor|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, [[https://www.sciencedirect.com/science/article/pii/S100757041930125X?via%3Dihub|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, {{ ::numerical_method_for_the_time-fractional_porous_medium_equation.pdf | PDF}}, [[https://epubs.siam.org/doi/abs/10.1137/18M1192561|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, [[https://www.sciencedirect.com/science/article/pii/S0022247X18301768|www]] * **Numerical method for Volterra equation with a power-type nonlinearity**, Applied Mathematics and Computation 337 (2018), 452-460, [[https://www.sciencedirect.com/science/article/pii/S0096300318304454|www]] * **Numerical schemes for integro-differential equations with Erdelyi-Kober fractional operator** (with Sz. Sobieszek), Numerical Algorithms 76(1) (2017), pp. 125-150, [[http://link.springer.com/article/10.1007/s11075-016-0247-z|www]], * **Diffusivity identification in a nonlinear time-fractional diffusion equation**, Fractional Calculus and Applied Analysis 19(4) (2016), pp. 883-866, [[https://www.degruyter.com/view/j/fca.2016.19.issue-4/fca-2016-0046/fca-2016-0046.xml|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 , [[http://www.sciencedirect.com/science/article/pii/S1007570415000064|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, {{::approximation_of_the_erdelyi-kober_operator_with_application_to_the_time-fractional_porous_medium_equation.pdf|PDF}}, [[http://epubs.siam.org/doi/abs/10.1137/130942450|www]] * **Eigenvalue asymptotics of a fractional boundary-value problem**, Applied Mathematics and Computation 241 (2014), 125-128, [[http://www.sciencedirect.com/science/article/pii/S0096300314006948|www]] * **Approximate self-similar solutions to a nonlinear diffusion equation with time-fractional derivative** (with H.Okrasińska), Physica D 261 (2013), 85-91, [[http://www.sciencedirect.com/science/article/pii/S0167278913002042|www]] * **A note on fractional Bessel function and its asymptotics** (with W.Okrasiński), Fractional Calculus and Applied Analysis 16 (3) (2013), 559-572, [[http://link.springer.com/article/10.2478%2Fs13540-013-0036-5|www]] * **On asymptotics of some fractional differential equations**, Mathematical Modelling and Analysis 18 (3) (2013), 358-373, [[http://www.tandfonline.com/doi/abs/10.3846/13926292.2013.804888#.Ush1DrSX2Nk|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, [[https://arxiv.org/pdf/2106.05140|arXiv]], [[https://reader.elsevier.com/reader/sd/pii/S0168927422001106?token=F68AAD859AD1F2151193E9F0091B92AC0AAFABB177ECDBEAB9C85226087A7A60BE8DF6D529F5373C4D675E5CD8ACFBBE&originRegion=eu-west-1&originCreation=20220505092901|Journal]] * **Hopf bifurcation in a conceptual climate model with ice-albedo and precipitation-temperature feedbacks**, Nonlinear Analysis: Real World Applications 51 (2020), 102967, [[https://www.sciencedirect.com/science/article/pii/S1468121819302032?dgcid=author|www]] * **Asymptotic analysis of internal relaxation-oscillations in a conceptual climate model**, IMA Journal of Applied Mathematics 85 (3) (2020), 467–494, [[https://academic.oup.com/imamat/advance-article/doi/10.1093/imamat/hxaa014/5827996?guestAccessKey=8c36f108-f810-4681-9ef0-e67cc2a7a02c|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), 105647[[https://www.sciencedirect.com/science/article/pii/S1007570420304779|www]] * **Asymptotic behaviour of a solution to a nonlinear equation modelling capillary rise** (with M. Świtała), Physica D 406 (2020), 132394, [[https://www.sciencedirect.com/science/article/pii/S0167278919306888|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, [[https://www.sciencedirect.com/science/article/pii/S0022247X20303991?via%3Dihub|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, [[https://www.sciencedirect.com/science/article/pii/S0167278917302452|www]] ===== Mathematics of sports ===== * **Discussion on angular asymmetry in the solutions of SLIP model** (with z P. Kowalczyki i Z. Wróblewska), Mathematica Applicanda 51(2) (2023), 233--237 [[https://wydawnictwa.ptm.org.pl/index.php/matematyka-stosowana/article/view/7194/6641|www]] * **Optimal strategy for trail running with nutrition and fatigue factors** (with B. Jaszczak), [[https://arxiv.org/abs/2401.02919|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, [[https://academic.oup.com/imamat/advance-article/doi/10.1093/imamat/hxad014/7116029?utm_source=authortollfreelink&utm_campaign=imamat&utm_medium=email&guestAccessKey=354e33e8-e41f-4390-9e67-9ad7dfc7c10b|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, [[https://www.sciencedirect.com/science/article/pii/S0167278922002585?dgcid=coauthor|Journal]] * **Asymptotic solution of a boundary value problem for a spring-mass model of legged locomotion**, Journal of Nonlinear Science 30, 2971–2988(2020), [[https://link.springer.com/article/10.1007/s00332-020-09641-w?wt_mc=Internal.Event.1.SEM.ArticleAuthorOnlineFirst|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, [[https://link.springer.com/article/10.1007/s11071-019-05462-z|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, [[http://www.sciencedirect.com/science/article/pii/S0010482516302098|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, [[http://www.sciencedirect.com/science/article/pii/S0010482516301469|www]] * **ODE/PDE Analysis of Corneal Curvature** (with W.E.Schiesser and G.W.Griffiths), Computers in Biology and Medicine 53 (2014), 30-41, [[http://www.sciencedirect.com/science/article/pii/S0010482514001681|www]] * **Nonliear Parameter Identification in Corneal Geometry Model** (with W.Okrasiński), Inverse Problems in Science and Engineering 23 (3) (2015), 443-456, [[http://www.tandfonline.com/doi/abs/10.1080/17415977.2014.922074#.U_YVE2PwqNk|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, [[http://www.sciencedirect.com/science/article/pii/S0022247X14000158|www]] * **Bessel function model of corneal topography** (with W.Okrasiński), Applied Mathematics and Computation 223 (2013), 436-443, [[http://www.sciencedirect.com/science/article/pii/S0096300313008588|www]] * **Regularization of an Ill-posed Problem in Corneal Topography** (with W.Okrasiński), Inverse Problems in Science and Engineering 21 (6) (2013), 1090–1097, [[http://www.tandfonline.com/doi/abs/10.1080/17415977.2012.753443#.Ush1RbSX2Nk|www]] * **A Nonlinear Mathematical Model of the Corneal Shape** (with W.Okrasiński), Nonlinear Analysis: Real World Applications 13 (2012), 1498-1505, [[http://www.sciencedirect.com/science/article/pii/S1468121811003221|www]] ===== Miscellaneous ===== * **The Bushell-Okrasiński inequality**, [[https://arxiv.org/pdf/2203.15256.pdf|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, [[https://www.sciencedirect.com/science/article/pii/S0096300318305277|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, [[http://www.tandfonline.com/eprint/5KsNgWGzcJj2tMkd5atZ/full|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, [[http://www.sciencedirect.com/science/article/pii/S0030399216300457?np=y|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, [[https://www.osapublishing.org/ao/abstract.cfm?uri=ao-55-12-B20|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, [[http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=2432183|www]] ====== Some Conference Presentations and Lectures ====== * Applied Mathematics and Mathematical Methods in Physics, Gdańsk, 2013, {{:dyfuzja.pdf|Anomalous diffusion}} * Between Theory and Applications - Mathematics in Action, Będlewo, 2013, {{:matokoang.pdf|Mathematics of human eye}} * ESGI 103 PhD Course //Modern Methods in Industrial Mathematics//, Technical University of Denmark, 2014, {{:lecture.pdf|Applications of the fractional calculus}}, {{:problems.pdf|Problem set}} In Polish: * Kobyla Góra, 2014, {{::kosmologia.pdf|Wszechświat w 30min}} (popularne wprowadzenie do kosmologii) * Kobyla Góra, 2014, {{::odwrotne.pdf|O matematyce na opak}} (krótko o problemach odwrotnych) ====== 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