[1]

Oldham K.B., Spanier J., The Fractional Calculus. Theory and Applications of Differentiation and Integration of Arbitrary Order, 1974, Academic Press, New York Google Scholar

[2]

Podlubny I., Fractional Differential Equations, 1999, Academic Press, New York Google Scholar

[3]

Kilbas A., Srivastava H., Trujillo J., Theory and Applications of Fractional Differential Equations, 2006, Math. Studies, North-Holland, New York Google Scholar

[4]

Hilfer R., Applications of Fractional Calculus in Physics, 2000, World Scientific, Singapore Google Scholar

[5]

Caputo M.,Mainardi F., A new dissipation model based on memory mechanism, Pure Appl. Geophys. 1971, 91, 134-147. Google Scholar

[6]

Baleanu D., Guvenc Z.B., Machado J.A.T., New Trends in Nanotechnology and Fractional Calculus Applications, 2010, Springer New York. Google Scholar

[7]

Uchaikin V., Fractional Derivatives for Physicists and Engineers, 2013, Springer H.D., London, New York. Google Scholar

[8]

Baleanu D., Jajarmi A., Hajipour M., A New Formulation of the Fractional Optimal Control Problems Involving Mittag-Leffler Nonsingular Kernel, J. Optim. Theory Appl., 2017, 175(3), 718-737. Google Scholar

[9]

Sun H.G., Hao X., Zhang Y., Baleanu D., Relaxation and diffusion models with non-singular kernels,Phys. A Stat. Mech. Appl., 2017, 468(1), 590-596. Google Scholar

[10]

Kumar D., Singh J., Baleanu D., Sushila, Analysis of regularized long-wave equation associated with a new fractional operator with Mittag-Leffler type kernel,Phys. A Stat. Mech. Appl., 2018, 492, 155-167. Google Scholar

[11]

Baleanu D., Jajarmi A., Asad J.H., Blaszczyk T., The motion of a bead sliding on a wire in fractional sense, Acta Phys. Pol. A, 2017, 131(6), 1561-1564. Google Scholar

[12]

Hajipour M., Jajarmi A., Baleanu D., An Efficient Non-standard Finite Difference Scheme for a Class of Fractional Chaotic Systems, J. Comput. Nonlinear Dyn., 2018, 13(2), 021013, 1-9. Google Scholar

[13]

Zhao D., Singh J., Kumar D., Rathore S., Yang X., An efficient computational technique for local fractional heat conduction equations in fractal media, J. Nonlinear Sci. Appl., 2017, 10(4), 1478-1486. Google Scholar

[14]

Kumar D., Singh J., Baleanu D., A new numerical algorithm for fractional Fitzhugh-Nagumo equation arising in transmission of nerve impulses, Nonlinear Dyn., 2018, 91(1), 307-317. Google Scholar

[15]

Singh J., Kumar D., Baleanu, D., On the analysis of chemical kinetics system pertaining to a fractional derivative with Mittag-Leffler type kernel, Chaos, 2017, 27(10), 103113. Google Scholar

[16]

Kumar D., Agarwal R.P., Singh J., A modified numerical scheme and convergence analysis for fractional model of Lienard’s equation, J. Comput. Appl. Math.,2018, 339, 405-413. Google Scholar

[17]

Khalil R., Al Horani M., Yousef A., Sababheh M., A new definition of fractional derivative, J. Comput. Appl. Math., 2014, 264, 65-70. Google Scholar

[18]

Katugampola U.N., A new fractional derivative with classical properties, 2014, arXiv:1410.6535v1. Google Scholar

[19]

Abdeljawad T., On conformable fractional calculus, J. Comput. Appl. Math., 2015, 279, 57-66. Google Scholar

[20]

Cenesiz Y., Baleanu D, Kurt A., Tasbozan O., New exact solutions of Burger’s type equations with conformable derivative, Waves in Random and complex Media, 2017,27(1),103-116. Google Scholar

[21]

Zhao D., Li T., On conformable delta fractional calculus on time scales, J. Math. Computer Sci., 2016, 16, 324-335. Google Scholar

[22]

Al Horani M., AbuHammad M., Khalil R., Variation of parameters for local fractional non-homogeneous linear differential equations, J. Math. Computer Sci., 2016, 16, 147-153. Google Scholar

[23]

Abu Hammad I, Khalil R., Fractional Fourier series with applications, Am. J. Comput. Applied Math., 2014, 4(6), 187-191. Google Scholar

[24]

Atangana A., Baleanu D., Alsaedi A., New properties of conformable derivative, Open Math., 2015, 13, 889-898. Google Scholar

[25]

Tarasov V.E., No violation of the Leibniz rule. No fractional derivative, Commun. Nonlinear Sci. Numer. Simulat., 2013, 18, 2945-2948. Google Scholar

[26]

Ahmad B., Batarfi H., Nieto J.J., Otero-Zarraquinos O., Shammakh W., Projectile motion via Riemann-Liouville calculus, Adv. Diff. Equations, 2015, 63(1), 1-14. Google Scholar

[27]

Ebaid A., Analysis of projectile motion in view of fractional calculus, Appl. Math. Modelling, 2011, 35, 1231-1239. Google Scholar

[28]

Sau Fa K., A falling body problem through the air in view of the fractional derivative approach, Physica A, 2005, 350, 199-206. Google Scholar

[29]

Rosales J.J., Gomez J.J., Guía M., Tkach V.I., Fractional Electromagnetic Waves, 2011, LFNM2011 International Conference on Laser and Fiber-Optical Networks Modeling 4-8 September, Kharkov, Ukraine. Google Scholar

[30]

Rosales J.J., Guía M., Gomez J.F., Tkach V.I., Fractional Electromagnetic Wave,Disc. Nonl. Compl.,2012, 1(4), 325-335. Google Scholar

[31]

Gomez-Aguilar J.F., Rosales-Garcia J.J., Bernal-Alvarado J.J., Cordova-Fraga T., Guzman-Cabrera R., Fractional Mechanical Oscillator, Rev. Mex. Fis., 2012, 58, 348-352. Google Scholar

[32]

Rosales García J.J., Guía M., Martínez J., Baleanu D., Motion of a particle in a resistive medium using fractional calculus approach, Proceed. Rom. Acad. Ser. A, 2013, 14, 42-47. Google Scholar

[33]

Rosales J.J., Guía M., Gomez F.,Aguilar F., Martínez J., Twodimensional fractional projectile motion in a resisting medium, Cent. Eur. J. Phys., 2014, 12(7), 517-520. Google Scholar

[34]

Ebaid A., Masaedeh B., El-Zahar E., A new fractional model for the falling body problem, Chin. Phys. Lett., 2017, 34(2), 020201 Google Scholar

[35]

Thornton S.T., Marion J.B., Classical dynamics of particles and systems, 2004, Thomson Brooks/Cole Google Scholar

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