Publications of Prof. Dr. Yuri Luchko


Books and books chapters

Fractional Diffusion and Wave Propagation. Chapter in: Freeden, Willi, Nashed, M. Zuhair, Sonar, Thomas (Eds.), Handbook of Geomathematics, Springer, Berlin, 2015, ISBN 978-3-642-54550-4, 1507-1545 Download

Fractional Diffusion and Wave Propagation. Chapter in: SpringerReference Handbook of Geomathematics, Springer, Berlin, 2014.

Anomalous Diffusion: Models, Their Analysis, and Interpretation. Chapter in: Advances in Applied Analysis, Series: Trends in Mathematics, ISBN 978-3-0348-0416-5, Birkhäuser, Basel, 2012, pp. 115-146.

Mathematische Modellierung mit MATLAB. Eine praxisorientierte Einführung, ISBN 978-3-8274-2398-6, Spektrum Akademischer Verlag, Heidelberg, 2010 (mit F. Haußer) Bestellung

Fractional-order viscoelasticity (FOV): Constitutive development using the fractional calculus: First annual report, NASA/TM 2002-211914, NASA's Glenn Research Center, Brook Rark, Ohio, December 2002 (with A.Freed and K.Diethelm) Download

The Hypergeometric Approach to Integral Transforms and Convolutions. Series: Mathematics and its applications, Vol. 287, ISBN 978-0-7923-2856-8, Kluwer Acad. Publ., Dordrecht/ Boston/London, 1994 (with S.Yakubovich) Bestellung

New families of Leibniz type rules for fractional calculus and their integral analogues. Chapter in: Recent Advances in Fractional Calculus. ISBN 978-0963815507, Sauk Rapids, Minnesota: Global Publ. Comp. 1993, pp. 248-291 (with H.M.Srivastava and S.Yakubovich).

Theory of the integral transformations with the Fox H-function as a kernel and some of its applications including operational calculus. PhD. thesis, Byelorussian State University, Minsk, 1993.


Papers in journals

The neutral-fractional telegraph equation. Math. Model. Nat. Phenom. 12 (2017), 51-67 (with L. Boyadjiev) Download

On Some New Properties of the Fundamental Solution to the Multi-Dimensional Space- and Time-Fractional Diffusion-Wave Equation. Mathematics 2017, 5, 76. Download

On the maximum principle for a time-fractional diffusion equation. Fract. Calc. Appl. Anal. 20 (2017), 1131-1145 (with M. Yamamoto) Download

FCAA special issue (FCAA–volume 20–5–2017). Fract. Calc. Appl. Anal. 20 (2017), 1053-1067 (with I. Podlubny) Download

Mellin integral transform approach to analyze the multidimensional diffusion-wave equations. Chaos, Solitons & Fractals, 102 (2017), 127-134 (with L. Boyadjiev) Download

Multi-dimensional α-fractional diffusion–wave equation and some properties of its fundamental solution. Computers & Mathematics with Applications 73 (2017), 2561–2572 (with L. Boyadjiev) Download

On the maximum principle for a time-fractional diffusion equation. arXiv:1702.07591, Analysis of PDEs (math.AP) 2017 (with M. Yamamoto) Download

Analyticity of solutions to a distributed order time-fractional diffusion equation and its application to an inverse problem. Computers & Mathematics with Applications 73 (2017), 1041–1052 (with Z. Li and M. Yamamoto) Download

Some new properties and applications of a fractional Fourier transform. Journal of Inequalities and Special Functions 8 (2017), 13-27 (with M. Manuela Rodrigues) Download

Modeling of financial processes with a space-time fractional diffusion equation of varying order. Fract. Calc. Appl. Anal. 19 (2016), 1414-1433 (with J. Korbel) Download

General time-fractional diffusion equation: Some uniqueness and existence results for the initial-boundary-value problems. Fract. Calc. Appl. Anal. 19 (2016), 676-695 (with M. Yamamoto) Download

A new fractional calculus model for the two-dimensional anomalous diffusion and its analysis. Math. Model. Nat. Phenom. 11 (2016), 1-17 Download

Entropy Production Rate of a One-Dimensional Alpha-Fractional Diffusion Process. Axioms 5 (2016) Download

Analysis of fractional diffusion equations of distributed order: Maximum principles and their applications. Analysis 36 (2016), 123-133 (with M. Al-Refai) Download

Time-fractional diffusion equation in the fractional Sobolev spaces. Fract. Calc. Appl. Anal. 18 (2015), 799–820 (with R. Gorenflo and M. Yamamoto) Download

Wave–diffusion dualism of the neutral-fractional processes. Journal of Computational Physics 293 (2015), 40–52 Download

Maximum principle for the multi-term time-fractional diffusion equations with the Riemann–Liouville fractional derivatives. Applied Mathematics and Computation 257(2015), 40-51 (with M. Al-Refai) Download

Operator theoretic approach to the Caputo derivative and the fractional diffusion equations. arXiv:1411.7289, Analysis of PDEs (math.AP) 2014 (with R. Gorenflo and M. Yamamoto) Download

Multi-dimensional fractional wave equation and some properties of its fundamental solution. Communications in Applied and Industrial Mathematics 6(2014), e-485 Download, E-print

Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations. Fract. Calc. Appl. Anal. 17(2014), 1114-1136 (with Z. Li and M. Yamamoto) Download

$\theta$-function method for a time-fractional reaction-diffusion equation. Journal of Algerian Mathematical Society 1(2014), 1-15 (with L. Zuo) Download

Cauchy and signaling problems for the time-fractional diffusion-wave equation. Journal of Vibration and Acoustics 136(2014), 050904 (with F. Mainardi) Download

Maximum principle for the fractional diffusion equations with the Riemann-Liouville fractional derivative and its applications. Fract. Calc. Appl. Anal. 17(2014), 483-498 (with M. Al-Refai) Download

Operational calculus for the Caputo-type fractional Erdélyi–Kober derivative and its applications. Integral Transforms and Special Functions 25(2014), 359-373 (with L.A-M. Hanna) Download

Comments on employing the Riesz-Feller derivative in the Schrödinger equation. The European Physical Journal Special Topics 222(2013), 1779-1794 (with B. Al-Saqabi and L. Boyadjiev) Download

Some properties of the fundamental solution to the signalling problem for the fractional diffusion-wave equation. Central European Journal of Physics 11(2013), 666–675 (with F. Mainardi) Download

Propagation speed of the maximum of the fundamental solution to the fractional diffusion–wave equation. Computers and Mathematics with Applications 66(2013), 774–784 (with F. Mainardi and Yu. Povstenko) Download, E-print

Uniqueness and reconstruction of an unknown semilinear term in a time-fractional reaction–diffusion equation. Inverse Problems 29(2013) 065019 (16pp) (with W. Rundell, M. Yamamoto and L. Zuo) Download

Riemann-Liouville and Caputo type multiple Erdélyi-Kober operators. Central European Journal of Physics 11(2013), 1314-1336 (with V. Kiryakova) Download

Fractional wave equation and damped waves. J. Math. Phys. 54(2013) 031505 Download, E-print

Fractional Schrödinger equation for a particle moving in a potential well. J. Math. Phys. 54(2013) 012111 Download

The Mellin integral transform in fractional calculus. Fract. Calc. Appl. Anal. 16(2013), 405-430 (with V. Kiryakova) Download

Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density. Fract. Calc. Appl. Anal. 16(2013), 297-316 (with R. Gorenflo and M. Stojanovic) Download

Verwendung schneller Wavelet-Transformation zum Detektieren von signifikanten Abweichungen im Rahmen eines Frühwarnsystems. Forum GeoBau 4(2013), 149-158 (with B. Resnik).

Fundamental solution of the fractional wave equation, its properties, and interpretation. Forum der Berliner mathematischen Gesellschaft 23(2012), 65-89.

Pattern formation in fractional reaction-diffusion systems with multiple homogeneous states. International Journal of Bifurcation and Chaos 22(2012), 1250087 (with B. Datsko and V. Gafiychuk) Download

Complex oscillations and limit cycles in autonomous two-component incommensurate fractional dynamical systems. Mathematica Balkanica 26(2012), 65-78 (with B. Datsko) Download

Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation. Fract. Calc. Appl. Anal. 15(2012), 141-160 Download, E-print

Modeling anomalous heat transport in geothermal reservoirs via fractional diffusion equations. International Journal on Geomathematics 1(2011), 257-276 (with A. Punzi) Download

Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation. Journal of Mathematical Analysis and Applications 374(2011), 538-548 Download

Modellierung anomaler Diffusionsprozesse mit fraktionalen Differentialgleichungen und ihre Analyse. In: Forschungsbericht 2011 der Beuth Hochschule für Technik Berlin. Wissenschaftlicher Verlag Berlin, 2011, 69-72.

Maximum principle and its application for the time-fractional diffusion equations. Fract. Calc. Appl. Anal. 14(2011), 110-124 Download

Anomalous diffusion models and their analysis. Forum der Berliner mathematischen Gesellschaft 19(2011), 53-85.

Professor Rudolf Gorenflo and his contribution to fractional calculus. Fract. Calc. Appl. Anal. 14 (2011), 3-18 (with F. Mainardi and S. Rogosin) Download

Numerical solution of fractional differential equations with a collocation method based on Müntz polynomials. Computers and Mathematics with Applications 62(2011), 918-929 (with S. Esmaeilia and M. Shamsia) Download

Modellierung anomaler Diffusionsprozesse mit fraktionalen Differentialgleichungen und ihre Analyse. Forum der Berliner mathematischen Gesellschaft 15(2010), 69-104.

Fractional Fourier transform in the framework of fractional calculus operators. Integral Transforms and Special Functions 21(2010), 779–795 (with A.A. Kilbas, H. Martínez and J.J. Trujillo). Download

Spectral method for solution of the fractional transport equation. Reports on Mathematical Physics 66(2010), 103-115 (with A. Kadem and D. Baleanu).

Some uniqueness and existence results for the initial-boundary-value problems for the generalized time-fractional diffusion equation. Computers and Mathematics with Applications 59(2010), 1766-1772. Download

Fractional models, non-locality, and complex systems. Computers and Mathematics with Applications 59(2010), 1048-1056 (with Margarita Rivero, Juan J. Trujillo, and M. Pilar Velasco). Download

The Wright function and its numerical evaluation. International J. of Pure and Applied Mathematics 64(2010), 567-575 (with J.J. Trujillo and M.P. Velasco)

Maximum principle and some uniqueness results for the generalized time-fractional diffusion equation. In: Forschungsbericht 2008/2009 der Beuth Hochschule für Technik Berlin. Beuth Hochschule für Technik Berlin, Berlin, 2009, 22-24. Download

Boundary value problems for the generalized time-fractional diffusion equation of distributed order. Fract. Calc. Appl. Anal. 12(2009), 409-422. Download

Operational method for the solution of fractional differential equations with generalized Riemann-Liouville fractional derivatives. Fract. Calc. Appl. Anal. 12(2009), 299-318 (with R. Hilfer and Z. Tomovski). Download

Maximum principle for the generalized time-fractional diffusion equation. Journal of Mathematical Analysis and Applications 351(2009), 218-223 Download

Fractional Fourier transform and some of its applications. Fract. Calc. Appl. Anal. 11(2008), 457-470 (with Hector Matrinez and Juan J. Trujillo). Download

Integral transforms of the Mellin convolution type and their generating operators. Integral Transforms and Special Functions 19(2008), 809 -851. Download

Algorithms for evaluation of the Wright function for the real arguments' values. Fract. Calc. Appl. Anal. 11(2008), 57-75. Download

Caputo-type modification of the Erdelyi-Kober fractional derivative. Fract. Calc. Appl. Anal. 10(2007), 249-267 (with J.J.Trujillo). Download

Algorithms for the fractional calculus: A selection of numerical methods. Computer Methods in Applied Mechanics and Engineering 194(2005), 743-773 (with K.Diethelm, N.Ford and A.Freed). Download

Operational rules for a mixed operator of the Erdelyi-Kober type. Fract. Calc. Appl. Anal. 7(2004), 339-364. Download

Numerical solution of linear multi-term differential equations of fractional order. Journal of Computational Analysis and Applications 6(2004), 243-263 (with K.Diethelm). Download

Computation of the Mittag-Leffler function and its derivatives. Fract. Calc. Appl. Anal. 5(2002), 491-518 (with R.Gorenflo and J.Loutchko). Download

The fundamental solution of the space-time fractional diffusion equation. Fract. Calc. Appl. Anal. 4 (2001), 153-192 (with F.Mainardi and G.Pagnini). Download

On the distribution of zeros of the Wright function. Integral Transforms and Special Functions 11(2001), 195-200. Download

On some boundary value problems for pseudo-differential equations with boundary operators of fractional order. Fract. Calc. Appl. Anal. 3(2000), 453-468 (with R.Gorenflo and S.Umarov). Download

On the Cauchy and multu-point problems for partial pseudo-differential equations of fractional order. Fract. Calc. Appl. Anal. 3(2000), 249-277 Download (with R.Gorenflo and S.Umarov).

Generalized Hankel transforms for hyper-Bessel differential operators. Comptes Rendus de l'Académie Bulgare des Sciences 53(2000), 17-20 (with V.Kiryakova). Download

Wright functions as scale-invariant solutions of the diffusion-wave equation. Journal of Computational and Applied Mathematics 11(2000), 175-191 (with R.Gorenflo and F.Mainardi). Download

On the asymptotics of zeros of the Wright function. Zeitschrift für Analysis und ihre Anwendungen 19(2000), 597-622. Download

Mapping between solutions of fractional diffusion-wave equations. Fract. Calc. Appl. Anal. 3(2000), 75-86 (with R.Gorenflo and A.Iskenderov). Download

Operational method in fractional calculus. Fract. Calc. Appl. Anal. 2(1999), 463-489. Download

Analytical properties and applications of the Wright function. Fract. Calc. Appl. Anal. 2(1999), 383-415 (with R.Gorenflo and F.Mainardi). Download

An operational method for solving fractional differential equations with the Caputo derivatives. Acta Mathematica Vietnamica 24(1999), 207-233 (with R Gorenflo). Download

On solvability of linear fractional differential equations in Banach spaces. Fract. Calc. Appl. Anal. 2(1999), 163-177 (with R.Gorenflo and P.P.Zabrejko). Download

Invariance of a partial differential equation of fractional order under the Lie group of scaling transformations. Journal of Mathematical Analysis and Applications 227(1998), 81-97 (with E.Buckwar). Download

Scale-invariant solutions of a partial differential equation of fractional order. Fract. Calc. Appl. Anal. 1(1998), 63-78 (with R.Gorenflo). Download

Operational method for solving integral equations with Gauss's hypergeometric function as a kernel. International Journal of Mathematical and Statistical Sciences 6(1997), 179-200 (with R.Gorenflo and H.M.Srivastava). Download

Operational method for solving generalized Abel integral equations of second kind. Integral Transforms and Special Functions 5(1997), 47-58 (with R.Gorenflo).

An operational method for solving fractional differential equations of an arbitrary real order. Panamerican Mathematical Journal 6(1996), 57-73 (with S.B.Hadid).

On generalized fractional calculus and its application to the solution of integro-differential equations. Journal of Fractional Calculus 7(1995), 69-88 (with M.A.Al-Bassam).

The exact solution of certain differential equations of fractional order by using operational calculus. Computers and Mathematics with Applications 29(1995), 73-85 (with H.M.Srivastava).

Operational properties of the convolution for the Kontorovich-Lebedev integral transform. Doklady Akademii Nauk Belarusi 38(1994), 19-23 (with S.Yakubovich).

Operational method of solution of some classes of integro-differential equations. Differentsial'nye Uravneniya 30(1994), 269-280 (in Russian); English translation in Differential Equations 30(1994), 247-256 (with S.Yakubovich).

The new Leibniz rules and their integral analogues. International Journal of Mathematical and Statistical Sciences 2(1993), 187-225 (with S.L.Kalla and S.Yakubovich).

The convolutional method for the development of new Leibniz rules involving fractional derivatives and of their integral analogues. Integral Transforms and Special Functions 1(1993), 119-134 (with H.M.Srivastava and S.Yakubovich).

Operational calculus for the generalized fractional differential operator and applications. Mathematica Balkanica 7(1993), 119-130 (with S.Yakubovich).

Generalizations of the Leibniz rule to integral convolutions. Doklady Akademii Nauk BSSR 35(1991), 111-115 (with S.Yakubovich).

Generalizations of the integral analog of the Leibniz rule on the G-convolutions. Extracta Mathematicae 6(1991), 119-122 (with S.Yakubovich).

Generating operators and convolutions for some integral transforms. Doklady Akademii Nauk BSSR 35(1991), 773-776 (with S.Yakubovich).


Papers in conference proceedings

Mathematische Modelle der anomalen Grundwasserdiffusion. In: Tagungsband zum Research Day 2015, Beuth Hochschule für Technik Berlin, 2015.

Bifurcation characteristics of fractional reaction-diffusion systems. In: AIP Conf. Proc. 1493 (2012), 290-297; doi: http://dx.doi.org/10.1063/1.4765503 (with B. Datsko and V. Gafiychuk).

Models of the neutral-fractional anomalous diffusion and their analysis. In: AIP Conf. Proc. 1493 (2012), 626-632; doi: http://dx.doi.org/10.1063/1.4765552

Neutral-fractional diffusion and damped waves. In: Proceedings of XXXII Dynamics Days Europe, Gothenburg, Sweden, 2-7 September 2012, Download

Some existence and uniqueness results for the time-fractional diffusion equations. In: Proceedings of TMSF 2011, the 6th International Conference Transform Methods and Special Functions, Sofia, Bulgaria, October 20-23, 2011 Download

Fractional nonlinear autonomous systems: stability analysis and limit cycles. In: Proceedings of TMSF 2011, the 6th International Conference Transform Methods and Special Functions, Sofia, Bulgaria, October 20-23, 2011 (with B. Datsko) Download

Nonlinear dynamics phenomena in fractional van der Pol-FitzHugh-Nagumo model. In: Proceedings of ENOC 2011, the 7th European Nonlinear Dynamics Conference, Rome, Italy, July 24 - 29, 2011 (with B. Datsko and V. Meleshko) Download

Complex pattern formation in bi-stable fractional reaction-diffusion systems. In: Proceedings of ENOC 2011, the 7th European Nonlinear Dynamics Conference, Rome, Italy, July 24 - 29, 2011 (with B. Datsko and V. Gafiychuk) Download

Maximum Principle for the Fractional Differential Equations and its Applications. In: Proceedings of FDA'10, the 4th IFAC Workshop on Fractional Differentiation and Its Applications, Badajoz, Spain, October 18-20, 2010.

Fractional calculus models for the anomalous diffusion processes and their analysis. In: AIP Conf. Proc. 1301 (2010), 623-635; doi: http://dx.doi.org/10.1063/1.3526664

The multi-index Mittag-Leffler functions and their applications for solving fractional order problems in applied analysis. In: AIP Conf. Proc. 1301 (2010), 597-613; doi: http://dx.doi.org/10.1063/1.3526661 (with V. Kiryakova).

Maximum principle for the generalized multi-term time-fractional diffusion equations and its applications. In: Proceedings of Symposium on Fractional Signals and Systems Lisbon'09, Lisbon, Portugal, November 4-7, 2009. Download

Initial-Boundary-Value Problems for the Generalized Time-Fractional Diffusion Equation. In: Proceedings of 3rd IFAC Workshop on Fractional Differentiation and its Applications (FDA08), Ankara, Turkey, November 5 - 7, 2008. Download

Hankel type transforms connected with the hyper-Bessel differential operators. In: Proceedings of Algebraic Analysis and Related Topics (Warsaw, 21-25 Sept.'99), Banach Center Publications (Inst. Math. PAN, Warsaw 2000) 53 (2000), 155-165 (with V.Kiryakova). Download

Operational method in fractional calculus. In: Proceedings of the International Workshop Transform Methods and Special Functions (TMSF99), Blagoevgrad, Bulgaria, 13-20 August 1999, 463-489. Download

Analytical properties and applications of the Wright function. In: Proceedings of the International Workshop Transform Methods and Special Functions (TMSF99), Blagoevgrad, Bulgaria, 13-20 August 1999, 383-415 (with R.Gorenflo and F.Mainardi). Download

Convolutions of the generalized fractional integration operators. In: Proceedings of 5-th Intern. Conf. Complex Analysis and Appl.'91, Sofia: Publishing House of the Bulgarian Academy, 1993, 199-211 (with S.Yakubovich).

Evaluation of integrals and series with respect to indices (parameters) of hypergeometric functions. In: Stephen M. Watt (Ed.), Proceedings of Intern. Symposium on Symbolic and Algebraic Comp. ISSAC'91, New York, NY: ACM Press 1991, 271-280 (with S.Yakubovich).