Math. Model. Nat. Phenom.
Volume 16, 2021
Fractional Dynamics in Natural Phenomena
Article Number 10
Number of page(s) 14
Published online 03 March 2021
  1. R. Almeida, N.R.O. Bastos and M.T.T. Monteiro, Modeling some real phenomena by fractional differential equations. Math. Methods Appl. Sci. 39 (2016) 4846–4855. [Google Scholar]
  2. M.A. Asiru, Sumudu transform and the solution of integral equation of convolution type. Int. J. Math. Educ. Sci. Technol. 32 (2001) 906–910. [Google Scholar]
  3. M.K. Bansal, P. Harjule, D. Kumar and J. Singh, Fractional kinetic equations associated with incomplete I-functions. Fractal Fract. 4 (2020) 19. [Google Scholar]
  4. F.B.M. Belgacem, A.A. Karaballi and S.L. Kalla, Analytical investigations of the Sumudu transform and applications to integral production equations. Math. Probl. Eng. 3 (2003) 103–118. [Google Scholar]
  5. F.B.M. Belgacem and A.A. Karaballi, Sumudu transform fundamental properties investigations and applications. Int. J. Stoch. Anal. 2006 (2006) 091083. [Google Scholar]
  6. S. Bhatter, A. Mathur, D. Kumar, K.S. Nisar and J. Singh, Fractional modified Kawahara equation with Mittag-Leffler law. Chaos Solitons Fract. 131 (2020) 109508. [Google Scholar]
  7. M. Caputo, Linear models of dissipation whose Q is almost frequency independent. Part II. Geophys. J. Int. 13 (1967) 529–539. [Google Scholar]
  8. V.B.L. Chaurasia and J. Singh, Application of Sumudu transform in Schrödinger equation occurring in Quantum mechanics. Appl. Math. Sci. 4 (2010) 2843–2850. [Google Scholar]
  9. A. Choudhary, D. Kumar and J. Singh, Numerical Simulation of a fractional model of temperature distribution and heat flux in the semi infinite solid. Alexandria Eng. J. 55 (2016) 87–91. [Google Scholar]
  10. H. Fazli and J.J. Nieto, Fractional Langevin equation with anti-periodic boundary conditions. Chaos Solitons Fract. 114 (2018) 332–337. [Google Scholar]
  11. V. Gill, Y. Singh, D. Kumar and J. Singh, Analytical study for fractional order mathematical model of concentration of Ca2+ in astrocytes cell with a composite fractional derivative. J. Multiscale Model. 11 (2020) 20500055. [Google Scholar]
  12. V. Gill, J. Singh and Y. Singh, Analytical solution of generalized space-time fractional advection-dispersion equation via coupling of Sumudu and Fourier transforms. To appear in: Front. Phys. 6 (2019) 1–6 doi: 10.3389/fphy.2018.00151. [Google Scholar]
  13. A. Goswami, Sushila, J. Singh and D. Kumar, Numerical computation of fractional Kersten-Krasil’shchik coupled KdV-mKdV System arising in multi-component plasmas. AIMS Math. 5 (2020) 2346–2368. [Google Scholar]
  14. E.M. Haacke, R.W. Brown, M.R. Thompson and R. Venkatesan, Magnetic Resonance Imaging: Physical Principles and Sequence Design. Wiley, New York (1999). [Google Scholar]
  15. R. Hilfer,Applications of Fractional Calculus in Physics. World Scientific Publishing Company, Singapore-New Jersey-Hong Kong (2000) 87–130. [Google Scholar]
  16. J. Hristov, Linear viscoelastic responses and constitutive equations in terms of fractional operators with non-singular kernels. Eur. Phys. J. Plus 134 (2019) 283. [Google Scholar]
  17. E. Ilhan and I.O. Kıymazb, A generalization of truncated M-fractional derivative and applications to fractional differential equations. Appl. Math. Nonlinear Sci. 5 (2020) 171–188. [Google Scholar]
  18. D. Kumar, J. Singh and D. Baleanu, On the analysis of vibration equation involving a fractional derivative with Mittag-Leffler law. Math. Methods Appl. Sci. 43 (2020) 443–457. [Google Scholar]
  19. R.L. Magin, O. Abdullah, D. Baleanu and X.J. Zhou, Anomalous diffusion expressed through fractional order differential operatorsin the Bloch-Torrey equation. J. Magn Reson. 190 (2008) 255–270. [Google Scholar]
  20. R. Magin, X. Feng and D. Baleanu, Solving the fractional order Bloch equation. Wiley. Inter. Sci. 34A (2009) 16–23. [Google Scholar]
  21. K.S. Miller and B. Ross, An Introduction to the fractional Calculus and Fractional Differential Equations. Wiley, New York (1993). [Google Scholar]
  22. I. Petras, Modelling and numerical analysis of fractional order Bloch equations. Comput. Math. Appl. 6 (2011) 341–356. [Google Scholar]
  23. C.M.A. Pinto and A.R.M. Carvalho, Fractional dynamics of an infection model with time-varying drug exposure. J. Computat. Nonlinear Dyn. 13 (2018) 090904. [Google Scholar]
  24. A.S.V. Ravi Kanth and N. Garg, Analytical solutions of the Bloch equation via fractional operators with non-singular kernels, in: Applied Mathematics and Scientific Computing. Trends in Mathematics, edited by B. Rushi Kumar et al. Springer Nature Switzerland (2019). [Google Scholar]
  25. T. Sandev, R. Metzler and Z. Tomovski, Fractional diffusion equation with a generalized Riemann–Liouville time fractional derivative. J. Phys. A: Math. Theor. 44 (2011) 255203. [Google Scholar]
  26. J. Singh, D. Kumar, D. Baleanu and S. Rathore, An efficient numerical algorithm for the fractional Drinfeld-Sokolov-Wilson equation. Appl. Math. Comput. 335 (2018) 12–24. [Google Scholar]
  27. J. Singh, D. Kumar and D. Baleanu, A new analysis of fractional fish farm model associated with Mittag-Leffler type Kernel. Int. J. Biomath. 13 (2020) 2050010. [Google Scholar]
  28. J. Singh, H.K. Jassim and D. Kumar, An efficient computational technique for local fractional Fokker Planck equation. Physica A 555 (2020) 124525. [Google Scholar]
  29. T.A. Sulaiman, M. Yavuz, H. Bulut and H.M. Baskonus, Investigation of the fractional coupled viscous Burgers’ equation involving Mittag-Leffler kernel. Physica A 527 (2019) 121–126. [Google Scholar]
  30. Z. Tomovski, R. Hilfer and H.M. Srivastava, Fractional and operational calculus with generalized fractional derivative operators and Mittag-Leffler type functions. Integral Trans. Special Funct. 21 (2010) 797–814. [Google Scholar]
  31. P. Veeresha, D.G. Prakasha, J. Singh, D. Kumar and D. Baleanu, Fractional Klein-Gordon-Schrödinger equations with Mittag-Leffler memory. Chin. J. Phys. 68 (2020) 65–78. [Google Scholar]
  32. G.K. Watugala, Sumudu transform – a new integral transform to solve differential equations and control engineering problems. Math. Eng. Ind. 6 (1998) 319–329. [Google Scholar]
  33. B.J. West, M. Bolgona, P. Grigolini, Physics of Fractal Operators. Springer-Verlag, New York (2003). [CrossRef] [Google Scholar]
  34. X.J. Yang, A new integral transform operator for solving the heat-diffusion problem. Appl. Math. Lett. 64 (2017) 193–197. [Google Scholar]
  35. M. Yavuz and T Abdeljawad, Nonlinear regularized long-wave models with a new integral transformation applied to the fractionalderivative with power and Mittag-Leffler kernel. Adv Differ Equ. 2020 (2020) 367. [Google Scholar]
  36. M. Yavuz and N. Özdemir, European vanilla option pricing model of fractional order without singular Kernel. Fract. Fract. 2 (2018) 3. [Google Scholar]
  37. M. Yavuz, Characterizations of two different fractional operators without singular kernel. MMNP 14 (2019) 302. [EDP Sciences] [Google Scholar]
  38. A. Yoku and S. Gülbahar, Numerical solutions with linearization techniques of the fractional Harry dym equation. Appl. Math. Nonlinear Sci. 4 (2019) 35–42. [Google Scholar]
  39. Q. Yu, F. Liu, I. Turner and K. Burrage, Numerical simulation of fractional Bloch equations. J. Comput. Appl. Math. 255 (2014) 635–651. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.