[1] 
Podlubny I 1999 Fractional Differential Equations of Mathematics in Science and Engineering (New York: Academic Press) Vol. 198

[2] 
Hilfer R 2000 Applications of Fractional Calculus in Physics (Singapore: World Scientific)

[3] 
Debnath L, Bhatta D 2006 Integral Transforms and Their Applications (Boca Raton: Chapman and Hall/CRC).

[4] 
Sabatier J, Agrawal O P and Tenreiro Machado J A (eds.) 2007 Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering (Netherlands: Springer)

[5] 
Ortigueira M D 2011 “Fractional Calculus for Scientists and Engineers”, Lecture Notes in Electrical Engineering 84 (Netherlands: Springer)

[6] 
Das S 2011 Functional Fractional Calculus (New York: Springer)

[7] 
Diethelm K, Ford N J and Freed A D 2002 Nonlinear Dynamics 29 3

[8] 
Liu F, Anh V and Turner I 2004 J. Comput. Appl. Math. 166 209

[9] 
Saha Ray S 2007 Phys. Scr. 75 article number 008 53

[10] 
Ortigueira M D and Tenreiro Machado J A 2006 Signal Processing 86 2503

[11] 
Saha Ray S 2008 Appl. Math. Comput. 202 544

[12] 
Tong B, He Y, Wei L and Zhang X 2012 Phys. Lett. A 376 2588

[13] 
Liu F, Zhuang P and Burrage K 2012 Comput. Math. Appl. 64 2990

[14] 
Saha Ray S 2012 Appl. Math. Comput. 218 5239

[15] 
Kadem A and Kılıçman A 2012 Abstr. Appl. Anal. 2012 1

[16] 
Gupta A K and Saha Ray S 2015 Appl. Math. Model. 39 5121

[17] 
Sahoo S and Saha Ray S 2015 Physica A: Statistical Mechanics and Its Applications 434 240

[18] 
Saha Ray S and Sahoo S 2015 Comput. Math. Appl. 70 158

[19] 
Gan W S 2007 Acoustical Imaging 28 445

[20] 
Kudryashov N A 2009 Commun. Nonlinear Sci. Numer. Simul. 14 1891

[21] 
Ryabov P N, Sinelshchikov D I and Kochanov M B 2011 Appl. Math. Comput. 218 3965

[22] 
Kudryashov N A 2012 Commun. Nonlinear Sci. Numer. Simul. 17 2248

[23] 
Kabir M M, Khajeh A, Aghdam E A and Koma A Y 2011 Math. Methods Appl. Sci. 34 244

[24] 
Ege S M and Misirli E 2014 Advances in Difference Equation 2014 135

[25] 
Taghizadeh N, Mirzazadeh M and Mahmoodirad A 2013 Indian J. Phys. 87 781

[26] 
Jumarie G 2005 Appl. Math. Lett. 18 739

[27] 
Jumarie G 2006 Comput. Math. Appl. 51 1367

[28] 
Jumarie G 2009 Appl. Math. Lett. 22 378

[29] 
Jumarie G 2013 Mathematics and Statistics 1 50

[30] 
Su W H, Yang X J, Jafari H and Baleanu D 2013 Advances in Difference Equations 2013 1

[31] 
Yang X J, Baleanu D and Srivastava H M 2015 Local Fractional Integral Transforms and Their Applications (London: Academic Press)

[32] 
He J H, Elagan S K and Li Z B 2012 Phys. Lett. A 376 257

[33] 
Güner O, Bekir A and Cevikel A C 2015 Eur. Phys. J. Plus 130 146

[34] 
Stakhov A and Rozin B 2005 Chaos, Solitons, and Fractals 23 379

[35] 
Pandir Y 2014 Appl. Math. Inform. Sci. 8 2237
