TY - STD TI - Agrawal, O.P.: Formulation of Euler-Lagrange equations for fractional variational problems, pp. 368–379 (2002). ID - ref1 ER - TY - JOUR AU - Agrawal, O. P. PY - 2007 DA - 2007// TI - Fractional variational calculus in terms of Riesz fractional derivatives JO - J. Phys. A VL - 24 UR - https://doi.org/10.1088/1751-8113/40/24/003 DO - 10.1088/1751-8113/40/24/003 ID - Agrawal2007 ER - TY - JOUR AU - Agrawal, O. P. PY - 2012 DA - 2012// TI - Generalized multiparameters fractional variational calculus JO - Int. J. Differential Equations VL - 2012 UR - https://doi.org/10.1155/2012/521750 DO - 10.1155/2012/521750 ID - Agrawal2012 ER - TY - JOUR AU - Almeida, R. AU - Torres, D. F. M. PY - 2009 DA - 2009// TI - Calculus of variations with fractional derivatives and fractional integrals JO - Appl. Math. Lett VL - 22 UR - https://doi.org/10.1016/j.aml.2009.07.002 DO - 10.1016/j.aml.2009.07.002 ID - Almeida2009 ER - TY - JOUR AU - Almeida, R. AU - Malinowska, A. B. AU - Torres, D. F. M. PY - 2010 DA - 2010// TI - A fractional calculus of variations for multiple integrals with application to vibrating string JO - J. Math. Phys VL - 51 UR - https://doi.org/10.1063/1.3319559 DO - 10.1063/1.3319559 ID - Almeida2010 ER - TY - BOOK AU - Atanackovic, T. M. AU - Pilipovic, S. AU - Stankovic, B. AU - Zorica, D. PY - 2014 DA - 2014// TI - Fractional Calculus with Applications in Mechanics: Wave Propagation, Impact and Variational Principles PB - Wiley-ISTE CY - London, Hoboken UR - https://doi.org/10.1002/9781118909065 DO - 10.1002/9781118909065 ID - Atanackovic2014 ER - TY - STD TI - Erdelyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.G.: Higher Transcendental Functions Volume 1. McGraw-Hill, New York, (1953), and Krieeger, Melbourne, Florida, (1981). ID - ref7 ER - TY - BOOK AU - Eringen, A. C. PY - 2002 DA - 2002// TI - Nonlocal Continuum Field Theories PB - Springer CY - New York ID - Eringen2002 ER - TY - JOUR AU - Jonscher, A. K. PY - 1977 DA - 1977// TI - The universal dielectric response JO - Nature VL - 267 UR - https://doi.org/10.1038/267673a0 DO - 10.1038/267673a0 ID - Jonscher1977 ER - TY - BOOK AU - Jonscher, A. K. PY - 1996 DA - 1996// TI - Universal Relaxation Law PB - Chelsea Dielectrics CY - London ID - Jonscher1996 ER - TY - STD TI - Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations (2006). ID - ref11 ER - TY - JOUR AU - Korabel, N. AU - Zaslavsky, G. M. AU - Tarasov, V. E. PY - 2007 DA - 2007// TI - Coupled oscillators with power-law interaction and their fractional dynamics analogues JO - Commun. Nonlin. Sci. Numeric. Simul VL - 12 UR - https://doi.org/10.1016/j.cnsns.2006.03.015 DO - 10.1016/j.cnsns.2006.03.015 ID - Korabel2007 ER - TY - STD TI - Mainardi, F.: Fractional calculus: Some basic problems in continuum and statistical mechanics. In: Carpinteri, A., Mainardi F (eds.)Fractals and Fractional Calculus in Continuum Mechanics, pp. 291–348. Springer, Wien and New York (1997). (arXiv:1201.0863). ID - ref13 ER - TY - BOOK AU - Mainardi, F. PY - 2010 DA - 2010// TI - Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models PB - World Scientific CY - Singapore UR - https://doi.org/10.1142/p614 DO - 10.1142/p614 ID - Mainardi2010 ER - TY - JOUR AU - Malinowska, A. B. AU - Torres, D. F. M. PY - 2011 DA - 2011// TI - Fractional calculus of variations for a combined Caputo derivative JO - Fractional Calculus Appl. Anal VL - 14 ID - Malinowska2011 ER - TY - JOUR AU - Mindlin, R. D. PY - 1964 DA - 1964// TI - Micro-structure in linear elasticity JO - Arch. Rational Mech. Anal VL - 16 UR - https://doi.org/10.1007/BF00248490 DO - 10.1007/BF00248490 ID - Mindlin1964 ER - TY - CHAP AU - Mindlin, R. D. ED - Kroner, E. PY - 1968 DA - 1968// TI - Theories of elastic continua and crystal lattice theories BT - Mechanics of Generalized Continua PB - Springer-Verlag CY - Berlin ID - Mindlin1968 ER - TY - JOUR AU - Nasrolahpour, H. PY - 2013 DA - 2013// TI - Fractional Lagrangian and Hamiltonian formulations in field theory Generalized multiparameters fractional variational calculus JO - Prespacetime J VL - 4 ID - Nasrolahpour2013 ER - TY - JOUR AU - Odzijewicz, T. AU - Malinowska, A. B. AU - Torres, D. F. M. PY - 2012 DA - 2012// TI - Fractional variational valculus with vlassical and vombined Caputo derivatives JO - Nonlinear Anal VL - 75 UR - https://doi.org/10.1016/j.na.2011.01.010 DO - 10.1016/j.na.2011.01.010 ID - Odzijewicz2012 ER - TY - JOUR AU - Riesz, M. PY - 1949 DA - 1949// TI - L’intégrale de Riemann-Liouville et le probléme de Cauchy JO - Acta Math VL - 81 UR - https://doi.org/10.1007/BF02395016 DO - 10.1007/BF02395016 ID - Riesz1949 ER - TY - BOOK AU - Rogula, D. PY - 1983 DA - 1983// TI - Nonlocal Theory of Material Media PB - Springer-Verlag CY - New York ID - Rogula1983 ER - TY - BOOK PY - 2007 DA - 2007// TI - Advances in Fractional Calculus. Theoretical Developments and Applications in Physics and Engineering PB - Springer CY - Dordrecht ID - ref22 ER - TY - STD TI - Samko, S.G., Kilbas, A.A., Marichev, O.I.: Integrals and Derivatives of Fractional Order and Applications (Nauka i Tehnika, Minsk, 1987); and Fractional Integrals and Derivatives Theory and Applications Gordon and Breach, New York (1993). ID - ref23 ER - TY - JOUR AU - Sedov, L. I. PY - 1965 DA - 1965// TI - Mathematical methods for constructing new models of continuous media JO - Russ. Math. Surv VL - 20 UR - https://doi.org/10.1070/RM1965v020n05ABEH001191 DO - 10.1070/RM1965v020n05ABEH001191 ID - Sedov1965 ER - TY - JOUR AU - Sedov, L. I. PY - 1968 DA - 1968// TI - Models of continuous media with internal degrees of freedom JO - J. Appl. Math. Mech VL - 32 UR - https://doi.org/10.1016/0021-8928(68)90001-4 DO - 10.1016/0021-8928(68)90001-4 ID - Sedov1968 ER - TY - STD TI - Sedov, L.I., Tsypkin, A.G.: Principles of the Microscopic Theory of Gravitation and Electromagnetism, Nauka, Moscow (1989). in Russian. ID - ref26 ER - TY - JOUR AU - Tarasov, V. E. PY - 2008 DA - 2008// TI - Universal electromagnetic waves in dielectrics JO - J. Phys.: Condensed Matter VL - 20 ID - Tarasov2008 ER - TY - JOUR AU - Tarasov, V. E. PY - 2009 DA - 2009// TI - Fractional integro-differential equations for electromagnetic waves in dielectric media JO - Theor. Math. Phys VL - 158 UR - https://doi.org/10.1007/s11232-009-0029-z DO - 10.1007/s11232-009-0029-z ID - Tarasov2009 ER - TY - BOOK AU - Tarasov, V. E. PY - 2011 DA - 2011// TI - Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media PB - Springer CY - New York ID - Tarasov2011 ER - TY - JOUR AU - Tarasov, V. E. PY - 2013 DA - 2013// TI - Review of some promising fractional physical models JO - Int. J. Modern Phys. B VL - 27 UR - https://doi.org/10.1142/S0217979213300053 DO - 10.1142/S0217979213300053 ID - Tarasov2013 ER - TY - JOUR AU - Tarasov, V. E. PY - 2013 DA - 2013// TI - Lattice model with power-law spatial dispersion for fractional elasticity JO - Central Eur. J. Phys VL - 11 ID - Tarasov2013 ER - TY - JOUR AU - Tarasov, V. E. PY - 2014 DA - 2014// TI - Lattice model of fractional gradient and integral elasticity: Long-range interaction of Grünwald-Letnikov-Riesz type JO - Mech. Mater VL - 70 UR - https://doi.org/10.1016/j.mechmat.2013.12.004 DO - 10.1016/j.mechmat.2013.12.004 ID - Tarasov2014 ER - TY - JOUR AU - Tarasov, V. E. PY - 2014 DA - 2014// TI - Lattice with long-range interaction of power-law type for fractional non-local elasticity JO - Int. J. Solids Struct VL - 51 UR - https://doi.org/10.1016/j.ijsolstr.2014.04.014 DO - 10.1016/j.ijsolstr.2014.04.014 ID - Tarasov2014 ER - TY - STD TI - Tarasov, V.E.: Fractional gradient elasticity from spatial dispersion law. ISRN Condensed Matter Phys. 2014. Article ID 794097, 13 pages (2014). (arXiv:1306.2572). ID - ref34 ER - TY - JOUR AU - Tarasov, V. E. PY - 2014 DA - 2014// TI - Fractional quantum field theory: From lattice to continuum JO - Adv. High Energy Phys VL - 2014 UR - https://doi.org/10.1155/2014/957863 DO - 10.1155/2014/957863 ID - Tarasov2014 ER - TY - JOUR AU - Tarasov, V. E. PY - 2014 DA - 2014// TI - General lattice model of gradient elasticity JO - Modern Phys. Lett. B VL - 28 UR - https://doi.org/10.1142/S0217984914500547 DO - 10.1142/S0217984914500547 ID - Tarasov2014 ER - TY - JOUR AU - Tarasov, V. E. PY - 2014 DA - 2014// TI - Toward lattice fractional vector calculus JO - J. Phys. A VL - 47 UR - https://doi.org/10.1088/1751-8113/47/35/355204 DO - 10.1088/1751-8113/47/35/355204 ID - Tarasov2014 ER - TY - JOUR AU - Tarasov, V. E. PY - 2015 DA - 2015// TI - Non-linear fractional field equations: weak non-linearity at power-law non-locality JO - Nonlinear Dynam VL - 80 UR - https://doi.org/10.1007/s11071-014-1342-0 DO - 10.1007/s11071-014-1342-0 ID - Tarasov2015 ER - TY - JOUR AU - Tarasov, V. E. PY - 2015 DA - 2015// TI - Lattice fractional calculus JO - Appl. Math. Comput VL - 257 ID - Tarasov2015 ER - TY - STD TI - Tarasov, V.E.: Three-dimensional lattice models with long-range interactions of Grünwald-Letnikov type for fractional generalization of gradient elasticity. Meccanica. 50 (2015). doi:10.1007/s11012-015-0190-4. UR - http://dx.doi.org/10.1007/s11012-015-0190-4 ID - ref40 ER - TY - JOUR AU - Tarasov, V. E. PY - 2015 DA - 2015// TI - Lattice model with nearest-neighbor and next-nearest-neighbor interactions for gradient elasticity JO - Discontinuity, Nonlinearity, Complexity VL - 4 UR - https://doi.org/10.5890/DNC.2015.03.002 DO - 10.5890/DNC.2015.03.002 ID - Tarasov2015 ER - TY - JOUR AU - Valerio, D. AU - Trujillo, J. J. AU - Rivero, M. AU - Tenreiro Machado, J. A. AU - Baleanu, D. PY - 2013 DA - 2013// TI - Fractional calculus: A survey of useful formulas JO - Eur. Phys. J. Spec. Topics VL - 222 UR - https://doi.org/10.1140/epjst/e2013-01967-y DO - 10.1140/epjst/e2013-01967-y ID - Valerio2013 ER - TY - BOOK AU - Zhou, Y. PY - 2014 DA - 2014// TI - Basic Theory of Fractional Differential Equations PB - World Scientific CY - Singapore UR - https://doi.org/10.1142/9069 DO - 10.1142/9069 ID - Zhou2014 ER -