# 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

**Fully discrete Galerkin scheme for a semilinear subdiffusion equation with nonsmooth data and time-dependent coefficient**(with K. Taźbierski), Computers and Mathematics with Applications 165 (2024) 217–223, arXiv**From Lévy walks to fractional material derivative: Pointwise representation and a numerical scheme**(with M. Teuerle), Communications in Nonlinear Science and Numerical Simulations 139 (2024), 108316. Journal**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**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**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**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

**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

**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

## 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

**Collocation method for a functional equation arising in behavioral sciences**(with J. Caballero, H.Okrasińska-Płociniczak and K. Sadarangani), Journal of Computational and Applied Mathematics 458 (2025), 116343, www**Existence and uniqueness of solutions in the Lipschitz space of a functional equation and its application to the behavior of the paradise fish**(with J. Caballero and K. Sadarangani), Applied Mathematics and Computation 477 (2024), 128798**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

- 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)

# 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