Citation: Ramazan Ozarslan, Erdal Bas, Dumitru Baleanu, Bahar Acay. Fractional physical problems including wind-influenced projectile motion with Mittag-Leffler kernel[J]. AIMS Mathematics, 2020, 5(1): 467-481. doi: 10.3934/math.2020031
[1] | K. Diethelm, A fractional calculus based model for the simulation of an outbreak of dengue fever, Nonlinear Dynam., 71 (2013), 613-619. doi: 10.1007/s11071-012-0475-2 |
[2] | S. Ullah, M. A. Khan and M. Farooq, A fractional model for the dynamics of TB virus, Chaos Soliton. Fract., 116 (2018), 63-71. doi: 10.1016/j.chaos.2018.09.001 |
[3] | I. Area, H. Batarfi, J. Losada, et al. On a fractional order Ebola epidemic model, Advances in Difference Equations, 2015 (2015), 278. |
[4] | H. Richard, Fractional calculus: an introduction for physicists, World Scientific, 2014. |
[5] | G. U. Varieschi, Applications of Fractional Calculus to Newtonian Mechanics, arXiv preprint arXiv:1712.03473, 2017. |
[6] | M. H. Heydari, Chebyshev cardinal functions for a new class of nonlinear optimal control problems generated by Atangana-Baleanu-Caputo variable-order fractional derivative, Chaos Soliton. Fract., 130 (2020), 109401. |
[7] | M. Hosseininia, M. H. Heydari, Meshfree moving least squares method for nonlinear variableorder time fractional 2D telegraph equation involving Mittag-Leffler non-singular kernel, Chaos Soliton. Fract., 127 (2019), 389-399. doi: 10.1016/j.chaos.2019.07.015 |
[8] | M. Hosseininia, M. H. Heydari, Legendre wavelets for the numerical solution of nonlinear variable-order time fractional 2D reaction-diffusion equation involving Mittag-Leffler nonsingular kernel, Chaos Soliton. Fract., 127 (2019), 400-407. doi: 10.1016/j.chaos.2019.07.017 |
[9] | E. Bonyah, A. Atangana, A. A. Elsadany, A fractional model for predator-prey with omnivore, Chaos: An Interdisciplinary Journal of Nonlinear Science, 29 (2019), 013136. |
[10] | A. Al-khedhairi, A. A. Elsadany, A. Elsonbaty, Modelling immune systems based on Atangana-Baleanu fractional derivative, Chaos Soliton. Fract., 129 (2019), 25-39. doi: 10.1016/j.chaos.2019.07.053 |
[11] | M. A. Khan, A. Khan, A. Elsonbaty, et al. Modeling and simulation results of a fractional dengue model, The European Physical Journal Plus, 134 (2019), 379. |
[12] | M. Yavuz, Characterizations of two different fractional operators without singular kernel, Math. Model. Nat. Pheno., 14 (2019), 302. |
[13] | M. Goyal, H. M. Baskonus, A. Prakash, An efficient technique for a time fractional model of lassa hemorrhagic fever spreading in pregnant women, The European Physical Journal Plus, 134 (2019), 482. |
[14] | T. Abdeljawad, Fractional operators with boundary points dependent kernels and integration by parts, Discrete Contin. Dyn. Syst. Ser. S, (2019), 351. |
[15] | E. Bas, R. Ozarslan, D. Baleanu, et al. Comparative simulations for solutions of fractional SturmLiouville problems with non-singular operators, Advances in Difference Equations, 2018 (2018), 350. |
[16] | A. Yusuf, M. Inc, A. I. Aliyu, et al. Efficiency of the new fractional derivative with nonsingular Mittag-Leffler kernel to some nonlinear partial differential equations, Chaos Soliton. Fract., 116 (2018), 220-226. doi: 10.1016/j.chaos.2018.09.036 |
[17] | E. Bas, The Inverse Nodal problem for the fractional diffusion equation, Acta Scientiarum. Technology, 37 (2015), 251-257. doi: 10.4025/actascitechnol.v37i2.17273 |
[18] | T. Abdeljawad, A Lyapunov type inequality for fractional operators with nonsingular Mittag-Leffler kernel, J. Inequal. Appl., 2017 (2017), 130. |
[19] | M. Caputo, F. Mainardi, A new dissipation model based on memory mechanism, Pure Appl. Geophys., 91 (1971), 134-147. doi: 10.1007/BF00879562 |
[20] | R. L. Magin, O. Abdullah, D. Baleanu, et al. Anomalous diffusion expressed through fractional order differential operators in the Bloch Torrey equation, J. Magn. Reson., 190 (2008), 255-270. doi: 10.1016/j.jmr.2007.11.007 |
[21] | V. V. Uchaikin, Fractional derivatives for physicists and engineers, Berlin: Springer, 2013. |
[22] | R. L. Magin, Fractional calculus in bioengineering, Redding: Begell House, 2006. |
[23] | A. K. Golmankhaneh, A. M. Yengejeh and D. Baleanu, On the fractional Hamilton and Lagrange mechanics, Int. J. Theor. Phys., 51 (2012), 2909-2916. doi: 10.1007/s10773-012-1169-8 |
[24] | D. G. Prakasha, P. Veeresha, H. M. Baskonus, Analysis of the dynamics of hepatitis E virus using the Atangana-Baleanu fractional derivative, The European Physical Journal Plus, 134 (2019), 241. |
[25] | W. Gao, B. Ghanbari, H. M. Baskonus, New numerical simulations for some real world problems with Atangana-Baleanu fractional derivative, Chaos Soliton. Fract., 128 (2019), 34-43. doi: 10.1016/j.chaos.2019.07.037 |
[26] | M. Yavuz, N. Ozdemir, H. M. Baskonus, Solutions of partial differential equations using the fractional operator involving Mittag-Leffler kernel, The European Physical Journal Plus, 133 (2018), 215. |
[27] | J. F. Gomez-Aguilar, J. J. Rosales-García, J. J. Bernal-Alvarado, et al. Fractional mechanical oscillators, Revista mexicana de física, 58 (2012), 348-352. |
[28] | M. Caputo, M. Fabrizio, A new definition of fractional derivative without singular kernel, Progr. Fract. Differ. Appl, 1 (2015), 1-13. |
[29] | A. Atangana and D. Baleanu, New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model, Therm. Sci., 20 (2016), 757-763. doi: 10.2298/TSCI160112019H |
[30] | A. Ebaid, Analysis of projectile motion in view of fractional calculus, Appl. Math. Model., 35 (2011), 1231-1239. doi: 10.1016/j.apm.2010.08.010 |
[31] | A. O. Contreras, J. J. R. Garcia, L. M. Jimenez, et al. Analysis of projectile motion in view of conformable derivative, Open Phys., 16 (2018), 581-587. doi: 10.1515/phys-2018-0076 |
[32] | B. Ahmad, H. Batarfi, J. J. Nieto, et al. Projectile motion via Riemann-Liouville calculus, Advances in Difference Equations, 2015 (2015), 63. |
[33] | J. Losada, J. J. Nieto, Properties of a new fractional derivative without singular kernel, Progr. Fract. Differ. Appl, 1 (2015), 87-92. |
[34] | J. Rosales, M. Guía, F. F. Gómez, et al. Two dimensional fractional projectile motion in a resisting medium, Open Phys., 12 (2014), 517-520. |
[35] | F. M. Alharbi, D. Baleanu, A. Ebaid, Physical properties of the projectile motion using the conformable derivative, Chinese J. Phys., 58 (2019), 18-28. doi: 10.1016/j.cjph.2018.12.010 |
[36] | J. F. Gomez-Aguilar, R. F. Escobar-Jiménez, M. G. Lopez-Lopez, et al. Analysis of projectile motion: A comparative study using fractional operators with power law, exponential decay and Mittag-Leffler kernel, The European Physical Journal Plus, 133 (2018), 103. |
[37] | R. C. Bernardo, J. P. Esguerra, J. D. Vallejos, et al. Wind-influenced projectile motion, Eur. J. Phys., 36 (2015), 025016. |
[38] | E. Bas, R. Ozarslan, Real world applications of fractional models by Atangana-Baleanu fractional derivative, Chaos Soliton. Fract., 116 (2018), 121-125. doi: 10.1016/j.chaos.2018.09.019 |
[39] | I. Podlubny, Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Elsevier, 1998. |
[40] | S. Liang, R. Wu, L. Chen, Laplace transform of fractional order differential equations, Electron. J. Differ. Equ., 2015 (2015), 1-15. doi: 10.1186/s13662-014-0331-4 |