Hanna, Latif A-M.; Al-Kandari, Maryam; Luchko, Yuri Operational method for solving fractional differential equations with the left-and right-hand sided Erdélyi-Kober fractional derivatives. (English) Zbl 1441.34009 Fract. Calc. Appl. Anal. 23, No. 1, 103-125 (2020). MSC: 34A08 34A25 26A33 44A35 33E30 45J99 45D99 PDFBibTeX XMLCite \textit{L. A M. Hanna} et al., Fract. Calc. Appl. Anal. 23, No. 1, 103--125 (2020; Zbl 1441.34009) Full Text: DOI
Luchko, Yu. Subordination principles for the multi-dimensional space-time-fractional diffusion-wave equation. (English) Zbl 1461.35007 Theory Probab. Math. Stat. 98, 127-147 (2019) and Teor. Jmovirn. Mat. Stat. 98, 121-141 (2018). MSC: 35A08 35R11 26A33 35C05 35E05 35L05 45K05 60E99 PDFBibTeX XMLCite \textit{Yu. Luchko}, Theory Probab. Math. Stat. 98, 127--147 (2019; Zbl 1461.35007) Full Text: DOI arXiv
Li, Zhiyuan; Luchko, Yuri; Yamamoto, Masahiro Analyticity of solutions to a distributed order time-fractional diffusion equation and its application to an inverse problem. (English) Zbl 1409.35221 Comput. Math. Appl. 73, No. 6, 1041-1052 (2017). MSC: 35R11 35B65 35R30 PDFBibTeX XMLCite \textit{Z. Li} et al., Comput. Math. Appl. 73, No. 6, 1041--1052 (2017; Zbl 1409.35221) Full Text: DOI
Luchko, Yuri On some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation. (English) Zbl 1474.35666 Mathematics 5, No. 4, Paper No. 76, 16 p. (2017). MSC: 35R11 35C05 35E05 35L05 45K05 60E99 PDFBibTeX XMLCite \textit{Y. Luchko}, Mathematics 5, No. 4, Paper No. 76, 16 p. (2017; Zbl 1474.35666) Full Text: DOI
Boyadjiev, L.; Luchko, Yu. The neutral-fractional telegraph equation. (English) Zbl 1398.35262 Math. Model. Nat. Phenom. 12, No. 6, 51-67 (2017). MSC: 35R11 35C05 35E05 35L05 45K05 PDFBibTeX XMLCite \textit{L. Boyadjiev} and \textit{Yu. Luchko}, Math. Model. Nat. Phenom. 12, No. 6, 51--67 (2017; Zbl 1398.35262) Full Text: DOI
Boyadjiev, Lyubomir; Luchko, Yuri Mellin integral transform approach to analyze the multidimensional diffusion-wave equations. (English) Zbl 1374.35419 Chaos Solitons Fractals 102, 127-134 (2017). MSC: 35R11 35C05 35E05 35L05 35A22 PDFBibTeX XMLCite \textit{L. Boyadjiev} and \textit{Y. Luchko}, Chaos Solitons Fractals 102, 127--134 (2017; Zbl 1374.35419) Full Text: DOI
Boyadjiev, Lyubomir; Luchko, Yuri Multi-dimensional \(\alpha\)-fractional diffusion-wave equation and some properties of its fundamental solution. (English) Zbl 1386.35427 Comput. Math. Appl. 73, No. 12, 2561-2572 (2017). MSC: 35R11 35A08 PDFBibTeX XMLCite \textit{L. Boyadjiev} and \textit{Y. Luchko}, Comput. Math. Appl. 73, No. 12, 2561--2572 (2017; Zbl 1386.35427) Full Text: DOI
Luchko, Yuri Entropy production rate of a one-dimensional alpha-fractional diffusion process. (English) Zbl 1415.35283 Axioms 5, No. 1, Paper No. 6, 11 p. (2016). MSC: 35R11 35E05 35L05 45K05 PDFBibTeX XMLCite \textit{Y. Luchko}, Axioms 5, No. 1, Paper No. 6, 11 p. (2016; Zbl 1415.35283) Full Text: DOI
Luchko, Yu. A new fractional calculus model for the two-dimensional anomalous diffusion and its analysis. (English) Zbl 1393.35280 Math. Model. Nat. Phenom. 11, No. 3, 1-17 (2016). MSC: 35R11 35C05 35E05 35L05 PDFBibTeX XMLCite \textit{Yu. Luchko}, Math. Model. Nat. Phenom. 11, No. 3, 1--17 (2016; Zbl 1393.35280) Full Text: DOI Link
Korbel, Jan; Luchko, Yuri Modeling of financial processes with a space-time fractional diffusion equation of varying order. (English) Zbl 1354.91178 Fract. Calc. Appl. Anal. 19, No. 6, 1414-1433 (2016). MSC: 91G80 60H30 26A33 60E07 60G22 60J60 91B84 91G20 PDFBibTeX XMLCite \textit{J. Korbel} and \textit{Y. Luchko}, Fract. Calc. Appl. Anal. 19, No. 6, 1414--1433 (2016; Zbl 1354.91178) Full Text: DOI
Luchko, Yuri Wave-diffusion dualism of the neutral-fractional processes. (English) Zbl 1349.35402 J. Comput. Phys. 293, 40-52 (2015). MSC: 35R11 PDFBibTeX XMLCite \textit{Y. Luchko}, J. Comput. Phys. 293, 40--52 (2015; Zbl 1349.35402) Full Text: DOI
Li, Zhiyuan; Luchko, Yuri; Yamamoto, Masahiro Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations. (English) Zbl 1312.35184 Fract. Calc. Appl. Anal. 17, No. 4, 1114-1136 (2014). MSC: 35R11 35B40 35S11 44A10 PDFBibTeX XMLCite \textit{Z. Li} et al., Fract. Calc. Appl. Anal. 17, No. 4, 1114--1136 (2014; Zbl 1312.35184) Full Text: DOI
Luchko, Yuri; Mainardi, Francesco; Povstenko, Yuriy Propagation speed of the maximum of the fundamental solution to the fractional diffusion-wave equation. (English) Zbl 1381.35226 Comput. Math. Appl. 66, No. 5, 774-784 (2013). MSC: 35R11 35A08 PDFBibTeX XMLCite \textit{Y. Luchko} et al., Comput. Math. Appl. 66, No. 5, 774--784 (2013; Zbl 1381.35226) Full Text: DOI arXiv
Luchko, Yuri; Kiryakova, Virginia The Mellin integral transform in fractional calculus. (English) Zbl 1312.26016 Fract. Calc. Appl. Anal. 16, No. 2, 405-430 (2013). MSC: 26A33 44A20 33C60 33E30 44A10 PDFBibTeX XMLCite \textit{Y. Luchko} and \textit{V. Kiryakova}, Fract. Calc. Appl. Anal. 16, No. 2, 405--430 (2013; Zbl 1312.26016) Full Text: DOI
Gorenflo, Rudolf; Luchko, Yuri; Stojanović, Mirjana Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density. (English) Zbl 1312.35179 Fract. Calc. Appl. Anal. 16, No. 2, 297-316 (2013). MSC: 35R11 33E12 35S10 45K05 PDFBibTeX XMLCite \textit{R. Gorenflo} et al., Fract. Calc. Appl. Anal. 16, No. 2, 297--316 (2013; Zbl 1312.35179) Full Text: DOI