Kragujevac Journal of Mathematics
University of Kragujevac - Faculty of Science

[1]   B. B. Mandelbrot, The Fractal Geometry of Nature, WH Freeman, New York, 1983.

[2]   J. Kigami, Analysis on Fractals, Cambridge University Press, Cambridge, 2001.

[3]   K. Falconer, Techniques in Fractal Geometry, John Wiley and Sons, Hoboken, New Jersey, 1997.

[4]   U. Freiberg and M. Zahle, Harmonic calculus on fractals-a measure geometric approach I, Potential Anal. 16(3) (2002), 265–277. https://doi.org/10.1023/A:1014085203265

[5]   R. S. Strichartz, Differential Equations on Fractals: A Tutorial, Princeton University Press, Princeton, New Jersey, 2006.

[6]   C. Cattani, Fractals and hidden symmetries in DNA, Math. Probl. Eng. 2010 (2010), 1–32. https://doi.org/10.1155/2010/507056

[7]   M. Rodriguez-Vallejo, D. Montagud, J. A. Monsoriu, V. Ferrando and W. D. Furlan, Relative peripheral myopia induced by fractal contact lenses, Current Eye Research 43(12) (2018), 1514–1521. https://doi.org/10.1080/02713683.2018.1507043

[8]   P. Chowdhury, N. Shivakumara, H. A. Jalab, R. W. Ibrahim, U. Pal and T. Lu, A new fractal series expansion based enhancement model for license plate recognition, Signal Processing: Image Communication 89 (2020), 1–12. https://doi.org/10.1016/j.image.2020.115958

[9]   M. T. Barlow and E. A. Perkins, Brownian motion on the Sierpinski gasket, Probability Theory and Related Fields 79(4) (1988), 543–623. https://doi.org/10.1007/BF00318785

[10]   A. S. Balankin, A continuum framework for mechanics of fractal materials I: From fractional space to continuum with fractal metric, Eur. Phys. J. B 88(4) (2015), 1–14. https://doi.org/10.1140/epjb/e2015-60189-y

[11]   M. Zubair, M. Mughal and Q. Naqvi, Electromagnetic Fields and Waves in Fractional Dimensional Space, Springer, New York, 2012.

[12]   L. Nottale and J. Schneider, Fractals and nonstandard analysis, J. Math. Phys. 25(5) (1998), 1296–1300. https://doi.org/10.1063/1.526285

[13]   K. M. Kolwankar and A. D. Gangal, Local fractional Fokker-Planck equation, Phys. Rev. Lett. 80(2) (1998), 1–4. https://doi.org/10.1103/PhysRevLett.80.214

[14]   R. A. El-Nabulsi, Path integral formulation of fractionally perturbed Lagrangian oscillators on fractal, J. Stat. Phys. 172(6) (2018), 1617–1640. https://doi.org/10.1007/s10955-018-2116-8

[15]   R. W. Ibrahim and D. Baleanu, Analytic solution of the Langevin differential equations dominated by a Multibrot fractal set, Fractal and Fractional 5(2) (2021), 1–16. https://doi.org/10.3390/fractalfract5020050

[16]   S. Das, Functional Fractional Calculus, Springer Science Business Media, Berlin, 2011.

[17]   I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.

[18]   W. Chen, H. Sun, X. Zhang and K. Dean, Anomalous diffusion modeling by fractal and fractional derivatives, Comput. Math. Appl. 59 (2010), 1754–1758. https://doi.org/10.1016/j.camwa.2009.08.020

[19]   W. Sumelka and G. Voyiadjis, A hyperelastic fractional damage material model with memory, International Journal of Solids and Structures 124 (2017), 151–160. https://doi.org/10.1016/j.ijsolstr.2017.06.024

[20]   K. Golmankhaneh, On the fractal Langevin equation, Fractal and Fractional 3(1) (2019), 1–11. https://doi.org/10.3390/fractalfract3010011

[21]    R. W. Ibrahim, Analytic solutions of the generalized water wave dynamical equations based on time-space symmetric differential operator, Journal of Ocean Engineering and Science 5(2) (2020), 186–195. https://doi.org/10.1016/j.joes.2019.11.001

[22]   S. Seema and A. D. Gangal, Langevin equation on fractal curves, Fractals 24(3) (2016), 1–9. https://doi.org/10.1142/S0218348X16500286

[23]   S. Ahmed and B. Alghamdi, Multi-strip and multi-point Boundary conditions for fractional Langevin equation, Fractal and Fractional 4(2) (2020), 1–18. https://doi.org/10.3390/fractalfract4020018

[24]   F. Hossein, H. Sun and S. Aghchi, Existence of extremal solutions of fractional Langevin equation involving nonlinear boundary conditions, Int. J. Comput. Math. 2020 (2020), 1–10. https://doi.org/10.1080/00207160.2020.1720662

[25]   D. Rahmat, B. Agheli and J. J. Nieto, Langevin equation involving three fractional orders, J. Stat. Phys. 178(4) (2020), 986–995. https://doi.org/10.1007/s10955-019-02476-0

[26]   R. W. Ibrahim and D. Baleanu, Entire solutions of a class of algebraic Briot-Bouquet differential equations utilizing majority concept, Adv. Difference Equ. 2020(678) (2020), 1–12. https://doi.org/10.1186/s13662-020-03138-2

[27]   R. W. Ibrahim and D. Baleanu, Geometric behavior of a class of algebraic differential equations in a complex domain using a majorization concept, AIMS Mathematics 6(1) (2021), 806–820. https://doi:10.3934/math.2021049

[28]   G. Wallace and F. Lagugne-Labarthet, Advancements in fractal plasmonics: structures, optical properties, and applications, Analyst 144(1) (2019), 13–30. https://doi10.1039/C8AN01667D

[29]   A. Cherny, E. Anitas, V. Osipov and A. Kuklin, The structure of deterministic mass and surface fractals: theory and methods of analyzing small-angle scattering data, Physical Chemistry Chemical Physics 21(1) (2019), 12748–12762. https://doi.org/10.1039/C9CP00783K

[30]   J. Komjathy, R. Molontay and K. Simon, Transfinite fractal dimension of trees and hierarchical scale-free graphs, J. Complex Netw. 5(7) (2019), 764–791. https://doi.org/10.1093/comnet/cnz005

[31]   E. Vanden-Eijnden and G. Ciccotti, Second-order integrators for Langevin equations with holonomic constraints, Chemical Physics Letters 429(1) (2006), 310–316. https://doi.org/10.1016/j.cplett.2006.07.086

[32]   S. S. Miller and P. T. Mocanu. Differential Subordinations: Theory and Applications, CRC Press, 2000.

[33]    S. Lee, V. Ravichandran and S. Supramaniam, Initial coefficients of biunivalent functions, Abstr. Appl. Anal. 2014(640856) (2014), 1–15. https://doi.org/10.1155/2014/640856