
AIMS Mathematics, 2020, 5(1): 467481. doi: 10.3934/math.2020031
Research article Special Issues
Export file:
Format
 RIS(for EndNote,Reference Manager,ProCite)
 BibTex
 Text
Content
 Citation Only
 Citation and Abstract
Fractional physical problems including windinfluenced projectile motion with MittagLeffler kernel
1 Department of Mathematics, Science Faculty, Firat University, 23119 Elazig, Turkey
2 Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, Ankara, Turkey
3 Institute of Space Sciences, MagureleBucharest, Romania
Received: , Accepted: , Published:
Special Issues: Recent Advances in Fractional Calculus with Real World Applications
References
1. K. Diethelm, A fractional calculus based model for the simulation of an outbreak of dengue fever, Nonlinear Dynam., 71 (2013), 613619.
2. S. Ullah, M. A. Khan and M. Farooq, A fractional model for the dynamics of TB virus, Chaos Soliton. Fract., 116 (2018), 6371.
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 AtanganaBaleanuCaputo variableorder 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 MittagLeffler nonsingular kernel, Chaos Soliton. Fract., 127 (2019), 389399.
8. M. Hosseininia, M. H. Heydari, Legendre wavelets for the numerical solution of nonlinear variableorder time fractional 2D reactiondiffusion equation involving MittagLeffler nonsingular kernel, Chaos Soliton. Fract., 127 (2019), 400407.
9. E. Bonyah, A. Atangana, A. A. Elsadany, A fractional model for predatorprey with omnivore, Chaos: An Interdisciplinary Journal of Nonlinear Science, 29 (2019), 013136.
10. A. Alkhedhairi, A. A. Elsadany, A. Elsonbaty, Modelling immune systems based on AtanganaBaleanu fractional derivative, Chaos Soliton. Fract., 129 (2019), 2539.
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 nonsingular 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 MittagLeffler kernel to some nonlinear partial differential equations, Chaos Soliton. Fract., 116 (2018), 220226.
17. E. Bas, The Inverse Nodal problem for the fractional diffusion equation, Acta Scientiarum. Technology, 37 (2015), 251257.
18. T. Abdeljawad, A Lyapunov type inequality for fractional operators with nonsingular MittagLeffler 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), 134147.
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), 255270.
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), 29092916.
24. D. G. Prakasha, P. Veeresha, H. M. Baskonus, Analysis of the dynamics of hepatitis E virus using the AtanganaBaleanu 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 AtanganaBaleanu fractional derivative, Chaos Soliton. Fract., 128 (2019), 3443.
26. M. Yavuz, N. Ozdemir, H. M. Baskonus, Solutions of partial differential equations using the fractional operator involving MittagLeffler kernel, The European Physical Journal Plus, 133 (2018), 215.
27. J. F. GomezAguilar, J. J. RosalesGarcía, J. J. BernalAlvarado, et al. Fractional mechanical oscillators, Revista mexicana de física, 58 (2012), 348352.
28. M. Caputo, M. Fabrizio, A new definition of fractional derivative without singular kernel, Progr. Fract. Differ. Appl, 1 (2015), 113.
29. A. Atangana and D. Baleanu, New fractional derivatives with nonlocal and nonsingular kernel: theory and application to heat transfer model, Therm. Sci., 20 (2016), 757763.
30. A. Ebaid, Analysis of projectile motion in view of fractional calculus, Appl. Math. Model., 35 (2011), 12311239.
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), 581587.
32. B. Ahmad, H. Batarfi, J. J. Nieto, et al. Projectile motion via RiemannLiouville 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), 8792.
34. J. Rosales, M. Guía, F. F. Gómez, et al. Two dimensional fractional projectile motion in a resisting medium, Open Phys., 12 (2014), 517520.
35. F. M. Alharbi, D. Baleanu, A. Ebaid, Physical properties of the projectile motion using the conformable derivative, Chinese J. Phys., 58 (2019), 1828.
36. J. F. GomezAguilar, R. F. EscobarJiménez, M. G. LopezLopez, et al. Analysis of projectile motion: A comparative study using fractional operators with power law, exponential decay and MittagLeffler kernel, The European Physical Journal Plus, 133 (2018), 103.
37. R. C. Bernardo, J. P. Esguerra, J. D. Vallejos, et al. Windinfluenced projectile motion, Eur. J. Phys., 36 (2015), 025016.
38. E. Bas, R. Ozarslan, Real world applications of fractional models by AtanganaBaleanu fractional derivative, Chaos Soliton. Fract., 116 (2018), 121125.
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), 115.
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)