[1] B.L.J. Braaksma. Asymptotic expansions and analytic continuations for a class of Barnes-integrals, Compositio Mathematica 15, pp. 239-341. 1964.
[2] M. Caputo. Elasticita Dissipacione (Bologna: Zanichelli). 1969.
[3] A. Compte. Stochastic foundations of fractional dynamics, Physical Review E 53, pp. 4191¬4193. 1996.
[4] M.M. Dzherbashyan. Harmonic Analysis and Boundary Value Problems in the Complex Domain, Vol 65 ed I Gohberg (Basel: Birkhauser). 1993.
[5] A. Erdelyi, W. Magnus, F. Oberhettinger, and F.G. Tricomi. Higher Transcedential Functions 3 (New York, Toronto and London: McGraw-Hill Book Company. 1955.
[ 6] W. Feller. An Introduction to Probability Theory and Its Applications, Vol. II (Wiley, New York) 1968.
[7] K.M. Furati, M.D. Kassim, and N.e.-Tatar. Existence and uniqueness for a problem involving Hilfer fractional derivative, Computers and Mathematics with Applications 64, pp. 1616¬1626. 2012.
[ 8] M. Garg, A. Sharma, and P. Manohar. Linear space-time fractional reaction-diffusion equa¬tion with composite fractional derivative in time, Journal of Fractional Calculus and Ap¬plications 5, pp. 114-121. 2014.
[9] Y.-J. Hao, H.M. Srivastava, H. Jafari, and X.-J. Yang. Helmholtz and Diffusion Equations Associated with Local Fractional Derivative Operators Involving the Cantorian and Cantor-Type Cylindrical Coordinates, Advances in Mathematical Physics 2013, 754248. 2013.
[10] R. Hilfer. Fractional dynamics, irreversibility and ergodicity breaking, Chaos, Solitons and
Fractals 5, pp. 1475-1484. 1995.
REFERENCES
332
[11] R. Hilfer. Application of Fractional Calculus in Physics (Singapore: World Scientific Pub¬lishing Company). 2000.
[12] R. Hilfer. Experimental evidence for fractional time evolution in glass forming materials,
Chemical Physics 284, pp. 399-408. 2002.
[13] R. Hilfer. On fractional relaxation, Fractals 11, pp. 251-257. 2003.
[14] R. Hilfer, Y. Luchko, and Z. Tomovski. Operational method for the solution of fractional differential equations with generalized Riemann-Liouville fractional derivatives, Fractional
Calculus and Applied Analysis 12, pp. 299-318. 2009.
[15] S. Al-Homidan, R.A. Ghanam, and N.-e. Tatar. On a generalized diffusion equation arising in petroleum engineering, Advances in Difference Equations 2013, 349. 2013.
[16] G. Jumarie. Non-standard analysis and Liouville-Riemann derivative, Chaos, Solitons and
Fractals 12, pp. 2577-2587. 2001.
[17] A.A. Kilbas, M. Saigo, and R.K. Saxena. Generalized Mittag-Leffler function and generalized fractional calculus operators, Integral Transforms and Special Functions 15, pp. 31-49.
2004.
[18] A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo. Theory and Applications of Fractional Dif¬ferential Equations (Amsterdam: Elsevier). 2006.
[19] M.-H. Kim, G.-C. Ri, and H.-C. O. Operational method for solving multi-term fractional differential equations with the generalized fractional derivatives, Fractional Calculus and
Applied Analysis 17, pp. 79-95. 2014.
[20] J. Liang, W. Zhang, Y.Q. Chen, and I. Podlubny. Robustness of boundary control of frac¬tional wave equations with delayed boundary measurement using fractional order con¬troller and the Smith predictor, in: Proceedings of2005 ASME Design Engineering Technical Conferences, Long Beach, California, USA, 2005.
[21] J. Liang and Y.Q. Chen. Hybrid symbolic and numerical simulation studies of time-fractional order wave-diffusion systems, International Journal of Control 79, pp. 1462-1470. 2006.
[22] Y. Luchko. Fractional Schrödinger equation for a particle moving in apotential well, Journal
of Mathematical Physics 54, 012111. 2013.
[ 23] F. Mainardi. Fractional relaxation-oscillation and fractional diffusion-wave phenomena, Chaos, Solitons and Fractals 7, pp. 1461-1477. 1996.
[ 24] F. Mainardi. The fundamental solutions for the fractional diffusion-wave equation, Applied Mathematics Letters 9, pp. 23-28. 1996.
[25] F. Mainardi and R. Gorenflo. On Mittag-Leffler-type functions in fractional evolution pro¬cesses, Journal of Computational and Applied Mathematics 118, pp. 283-299. 2000.
REFERENCES
333
[26] F. Mainardi and R. Gorenflo. Time-fractional derivatives in relaxation processes: a tutorial survey, Fractional Calculus and Applied Analysis 10, pp. 269-308. 2007.
[27] F. Mainardi, G. Pagnini, and R.K. Saxena. Fox H functions in fractional diffusion, Journal of Computational and Applied Mathematics 178, pp. 321-331. 2005.
[28] H.J. Haubold, A.M. Mathai, and R.K. Saxena. Solutions offractional reaction-diffusion equations in terms ofthe H-function, Bulletin of the Astronomical Society of India 35, pp.
681-689. 2007.
[ 29] A.M. Mathai, R.K. Saxena, and H.J. Haubold. The H-function: Theory and Applications (New York: Springer). 2010.
[ 30] R. Metzler, E. Barkai, and J. Klafter. Anomalous diffusion and relaxation close to thermal equilibrium: a fractional Fokker-Planck equation approach, Physical Review Letters 82,
pp. 3563-3567. 1999.
[31] R. Metzler and J. Klafter. The random walk's guide to anomalous diffusion: a fractional dynamics approach, Physics Reports 339, pp. 1-77. 2000.
[ 32] R. Metzler and J. Klafter. The restaurant at the end ofthe random walk: recent develop¬ments in the description ofanomalous transport byfractional dynamics, Journal of Physics
A: Mathematical and General 37, pp. R161-R208. 2004.
[ 33] G. Pagnini, A. Mura, and F. Mainardi. Generalized fractional master equation for self-similar stochastic processes modelling anomalous diffusion, International Journal of
Stochastic Analysis 2012, 427383. 2012.
[34] I. Podlubny. Fractional Differential Equations, (San Diego: Acad. Press, 1999).
[35] T.R. Prabhakar. A singular integral equation with a generalized Mittag-Leffler function in the kernel, Yokohama Mathematical Journal 19, pp. 7-15. 1971.
[36] S.G. Samko, A.A. Kilbas, and O.I. Marichev. Fractional Integrals and Derivatives. Theory and Applications (New York et al: Gordon and Breach). 1993.
[ 37] M.S. Samuel and A. Thomas. On fractional Helmholtz equations, Fractional Calculus and Applied Analysis 13, pp. 295-308. 2010.
[ 38] T. Sandev, R. Metzler, and Z. Tomovski. Fractional diffusion equation with a generalized Riemann-Liouville time fractional derivative, Journal of Physics A: Mathematical and The¬oretical 44, pp. 255203. 2011
[39] T. Sandev and Z. Tomovski. The general time fractional wave equation for a vibrating string, Journal of Physics A: Mathematical and Theoretical 43, pp. 055204. 2010.
[40] B. Al-Saqabi, L. Boyadjiev, and Y. Luchko. Comments on employing the Riesz-Feller derivative in the Schrödinger equation, European Physical Journal 222, pp. 1779-1794. 2013.
REFERENCES
334
[ 41 ] R.K. Saxena. On a fractional master equation and a fractional diffusion equation, Mathe¬matics and Statistics 1, pp. 59-63. 2013.
[42] R.K. Saxena, A.M. Mathai, and H.J. Haubold. Unified fractional kinetic equation and a fractional diffusion equation, Astrophysics and Space Science 290, pp. 299-310. 2004.
[43] R.K. Saxena, A.M. Mathai, and H.J. Haubold. Fractional reaction-diffusion equations, As¬trophysics and Space Science 305, pp. 289-296. 2006.
[ 44] R.K. Saxena, A.M. Mathai, and H.J. Haubold. Solutions offractional reaction-diffusion equations in terms of Mittag-Leffler functions, International Journal of Scientifc Research
17, pp. 1-17. 2008.
[45] R.K. Saxena, A.M. Mathai, and H.J. Haubold. Computational solutions of unified fractional reaction-diffusion equations with composite fractional time derivative, arXiv:1210.1453v1.
[ 46] H.M. Srivastava and R.K. Saxena. Operators offractional integration and their applica¬tions, Applied Mathematics and Computation 118. pp. 1-52. 2001.
[ 47] H.M. Srivastava and Z. Tomovski. Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernel, Applied Mathematics and Computation
211, pp. 198-210. 2009.
[ 48] A. Thomas. On a fractional master equation, International Journal of Differential Equa¬tions 2011,346298. 2013.
[49] Z. Tomovski. Generalized Cauchytype problems for nonlinear fractional differential equa¬tions with composite fractional derivative operator, Nonlinear Analysis: Theory, Methods
and Applications 75, pp. 3364-3384. 2012.
[50] Z. Tomovski, R. Hilfer, and H.M. Srivastava. Fractional and operational calculus with gen¬eralized fractional derivative operators and Mittag-Leffler type functions, Integral Transforms and Special Functions 21, pp. 797-814. 2010.
[51] Z. Tomovski and T. Sandev. Effects of a fractional friction with power-law memory kernel on string vibrations, Computers and Mathematics with Applications 62, pp. 1554-1561.
2011.
[ 52] Z. Tomovski and T. Sandev. Fractional wave equation with a frictional memory kernel of Mittag-Leffler type, Applied Mathematics and Computation 218, pp. 10022-10031. 2012.
[ 53] Z. Tomovski and T. Sandev. Exact solutions for fractional diffusion equation in a bounded domain with different boundary conditions, Nonlinear Dynamics 71, pp. 671-683. 2013.
[ 54] Z. Tomovski, T. Sandev, R. Metzler, and J. Dubbeldam. Generalized space-time fractional diffusion equation with composite fractional time derivative, Physica A 391, pp. 2527-2542.
2012.
Thank you for copying data from http://www.arastirmax.com