-
S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications (Nauka Tekh., Minsk, 1987; Gordon and Breach, Yverdon, 1993).
-
V. V. Uchaikin, Method of Fractional Derivatives (Artishok, Ul’yanovsk, 2008) [in Russian].
-
R. Raghavan, “Fractional Diffusion: Performance of Fractured Wells”, J. Petrol. Sci. Eng. 92-93, 167-173 (2012).
-
D. Stan, F. del Teso, and J. L. Vázquez, “Finite and Infinite Speed of Propagation for Porous Medium Equations with Nonlocal Pressure”, J. Differ. Equ. 260 (2), 1154-1199 (2016).
-
C. Pozrikidis, The Fractional Laplacian (CRC Press, Boca Raton, 2016).
-
A. V. Abramyan, V. A. Nogin, and S. G. Samko, “Fractional Powers of the Operator -|x|²Δ in Lp Spaces”, Differ. Uravn. 32 (2), 275-276 (1996) [Differ. Equ. 32 (2), 281-283 (1996)]. EDN: PDGEIX
-
B. Barrios, E. Colorado, A. De Pablo, and U. Sánchez, “On Some Critical Problems for the Fractional Laplacian Operator”, J. Differ. Equ. 252 (11), 6133-6162 (2012).
-
H. Chen, P. Felmer, and A. Quaas, “Large Solutions to Elliptic Equations Involving Fractional Laplacian”, Annales de l’Institut Henri Poincaré (C), Analyse Non Linéaire 32 (6), 1199-1228 (2015). DOI: 10.1016/j.anihpc.2014.08.00
-
J. L. Vázquez, A. de Pablo, F. Quirós, and A. Rodriguez, “Classical Solutions and Higher Regularity for Nonlinear Fractional Diffusion Equations”, J. Eur. Math. Soc. 19 (7), 1949-1975 (2017).
-
E. C. Aifantis, "Fractional Generalizations of Gradient Mechanics", in Handbook of Fractional Calculus with Applications (De Gruyter, Berlin, 2019), Vol. 4, pp. 241-262.
-
A. D. Polyanin, Linear Equations of Mathematical Physics (Fizmatlit, Moscow, 2001) [in Russian]. EDN: MVANPN
-
L. Greengard and V. Rokhlin, "A Fast Algorithm for Particle Simulations", J. Comput. Phys. 135 (2), 280-292 (1997).
-
N. A. Gumerov and R. Duraiswami, Fast Multipole Methods for the Helmholtz Equation in Three Dimensions (Elsevier, Amsterdam, 2005).
-
N. S. Belevtsov and S. Yu. Lukashchuk, "Multipole Expansion of the Fundamental Solution of a Fractional Degree of the Laplace Operator", in Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. (VINITI, Moscow, 2020), Vol. 176, pp. 26-33.
-
N. S. Belevtsov and S. Yu. Lukashchuk, "A Parallel Numerical Algorithm for Solving Fractional Poisson Equation", in Proc. Int. Conf. on Parallel Computational Technologies, Kaliningrad, Russia, April 2-April 4, 2019 (South Ural State Univ., Chelyabinsk, 2019), pp. 165-174.
-
N. S. Belevtsov and S. Yu. Lukashchuk, "Factorization of the Fundamental Solution to Fractional Helmholtz Equation", Lobachevskii J. Math. 42 (1), 57-62 (2021). EDN: HXITXD
-
A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 2: Special Functions (Nauka, Moscow, 1983; Gordon and Breach, New York, 1986).
-
A. A. Kilbas and M. Saigo, H-transforms: Theory and Applications (CRC Press, Boca Raton, 2004).
-
R. Gorenflo, J. Loutchko, and Y. Luchko, "Computation of the Mittag-Leffler Function Eα, β(z) and Its Derivative", Fract. Calc. Appl. Anal. 5 (4), 491-518 (2002).
-
Y. Luchko, "Algorithms for Evaluation of the Wright Function for the Real Arguments' Values", Fract. Calc. Appl. Anal. 11 (1), 57-75 (2008).
-
R. D. Mindlin and N. N. Eshel, "On First Strain-Gradient Theories in Linear Elasticity", Int. J. Solids Struct. 4 (1), 109-124 (1968).
-
C. Q. Ru and E. C. Aifantis, "A Simple Approach to Solve Boundary-Value Problems in Gradient Elasticity", Acta Mech. 101 (1), 59-68 (1993).
-
B. G. Korenev, Introduction to the Theory of Bessel Functions (Nauka, Moscow, 1971) [in Russian].