Garra, R.; Consiglio, A.; Mainardi, F. A note on a modified fractional Maxwell model. (English) Zbl 1507.74065 Chaos Solitons Fractals 163, Article ID 112544, 5 p. (2022). MSC: 74B05 74D05 74L10 76A10 26A33 35R11 33E12 PDFBibTeX XMLCite \textit{R. Garra} et al., Chaos Solitons Fractals 163, Article ID 112544, 5 p. (2022; Zbl 1507.74065) Full Text: DOI arXiv
Consiglio, Armando; Mainardi, Francesco On the evolution of fractional diffusive waves. (English) Zbl 1469.35219 Ric. Mat. 70, No. 1, 21-33 (2021). MSC: 35R11 26A33 33E12 34A08 35-03 65D20 60J60 74J05 PDFBibTeX XMLCite \textit{A. Consiglio} and \textit{F. Mainardi}, Ric. Mat. 70, No. 1, 21--33 (2021; Zbl 1469.35219) Full Text: DOI arXiv
Colombaro, Ivano; Garra, Roberto; Giusti, Andrea; Mainardi, Francesco Scott-Blair models with time-varying viscosity. (English) Zbl 1407.76007 Appl. Math. Lett. 86, 57-63 (2018). MSC: 76A10 PDFBibTeX XMLCite \textit{I. Colombaro} et al., Appl. Math. Lett. 86, 57--63 (2018; Zbl 1407.76007) Full Text: DOI arXiv
Garra, Roberto; Giusti, Andrea; Mainardi, Francesco The fractional Dodson diffusion equation: a new approach. (English) Zbl 1403.35314 Ric. Mat. 67, No. 2, 899-909 (2018). MSC: 35R11 33E12 45K05 PDFBibTeX XMLCite \textit{R. Garra} et al., Ric. Mat. 67, No. 2, 899--909 (2018; Zbl 1403.35314) Full Text: DOI arXiv
Garrappa, Roberto; Rogosin, Sergei; Mainardi, Francesco On a generalized three-parameter Wright function of Le Roy type. (English) Zbl 1374.33019 Fract. Calc. Appl. Anal. 20, No. 5, 1196-1215 (2017). MSC: 33E12 30D10 30F15 35R11 PDFBibTeX XMLCite \textit{R. Garrappa} et al., Fract. Calc. Appl. Anal. 20, No. 5, 1196--1215 (2017; Zbl 1374.33019) Full Text: DOI arXiv
Vitali, Silvia; Castellani, Gastone; Mainardi, Francesco Time fractional cable equation and applications in neurophysiology. (English) Zbl 1374.92025 Chaos Solitons Fractals 102, 467-472 (2017). MSC: 92C20 92C30 35Q92 35R11 PDFBibTeX XMLCite \textit{S. Vitali} et al., Chaos Solitons Fractals 102, 467--472 (2017; Zbl 1374.92025) Full Text: DOI arXiv
Garrappa, Roberto; Mainardi, Francesco; Guido, Maione Models of dielectric relaxation based on completely monotone functions. (English) Zbl 1499.78010 Fract. Calc. Appl. Anal. 19, No. 5, 1105-1160 (2016). MSC: 78A48 26A33 33E12 34A08 26A48 44A10 PDFBibTeX XMLCite \textit{R. Garrappa} et al., Fract. Calc. Appl. Anal. 19, No. 5, 1105--1160 (2016; Zbl 1499.78010) Full Text: DOI arXiv
Garrappa, Roberto; Mainardi, Francesco On Volterra functions and Ramanujan integrals. (English) Zbl 1342.45001 Analysis, München 36, No. 2, 89-105 (2016). MSC: 45D05 45E05 33E20 33E50 33F05 65D20 PDFBibTeX XMLCite \textit{R. Garrappa} and \textit{F. Mainardi}, Analysis, München 36, No. 2, 89--105 (2016; Zbl 1342.45001) Full Text: DOI arXiv
Gorenflo, Rudolf; Mainardi, Francesco On the fractional Poisson process and the discretized stable subordinator. (English) Zbl 1415.60051 Axioms 4, No. 3, 321-344 (2015). MSC: 60G55 60G22 60K05 PDFBibTeX XMLCite \textit{R. Gorenflo} and \textit{F. Mainardi}, Axioms 4, No. 3, 321--344 (2015; Zbl 1415.60051) Full Text: DOI arXiv
de Oliveira, Edmundo Capelas; Mainardi, Francesco; Vaz, Jayme jun. Fractional models of anomalous relaxation based on the Kilbas and Saigo function. (English) Zbl 1307.34007 Meccanica 49, No. 9, 2049-2060 (2014). MSC: 34A08 33E12 PDFBibTeX XMLCite \textit{E. C. de Oliveira} et al., Meccanica 49, No. 9, 2049--2060 (2014; Zbl 1307.34007) 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
Pagnini, Gianni; Mura, Antonio; Mainardi, Francesco Two-particle anomalous diffusion: probability density functions and self-similar stochastic processes. (English) Zbl 1339.60116 Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 371, No. 1990, Article ID 20120154, 11 p. (2013). MSC: 60J60 60G18 60G22 60G51 60G52 PDFBibTeX XMLCite \textit{G. Pagnini} et al., Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 371, No. 1990, Article ID 20120154, 11 p. (2013; Zbl 1339.60116) Full Text: DOI
Pagnini, Gianni; Mura, Antonio; Mainardi, Francesco Generalized fractional master equation for self-similar stochastic processes modelling anomalous diffusion. (English) Zbl 1260.60163 Int. J. Stoch. Anal. 2012, Article ID 427383, 14 p. (2012). MSC: 60J60 60G18 60G22 PDFBibTeX XMLCite \textit{G. Pagnini} et al., Int. J. Stoch. Anal. 2012, Article ID 427383, 14 p. (2012; Zbl 1260.60163) Full Text: DOI
Luchko, Yury; Mainardi, Francesco; Rogosin, Sergei Professor Rudolf Gorenflo and his contribution to fractional calculus. (English) Zbl 1273.01048 Fract. Calc. Appl. Anal. 14, No. 1, 3-18 (2011). MSC: 01A70 01A60 26-03 26A33 PDFBibTeX XMLCite \textit{Y. Luchko} et al., Fract. Calc. Appl. Anal. 14, No. 1, 3--18 (2011; Zbl 1273.01048) Full Text: DOI Link
Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni The \(M\)-Wright function in time-fractional diffusion processes: a tutorial survey. (English) Zbl 1222.60060 Int. J. Differ. Equ. 2010, Article ID 104505, 29 p. (2010). MSC: 60J60 26A33 60G17 35R11 PDFBibTeX XMLCite \textit{F. Mainardi} et al., Int. J. Differ. Equ. 2010, Article ID 104505, 29 p. (2010; Zbl 1222.60060) Full Text: DOI arXiv EuDML
Pagnini, Gianni; Mainardi, Francesco Evolution equations for the probabilistic generalization of the Voigt profile function. (English) Zbl 1179.82008 J. Comput. Appl. Math. 233, No. 6, 1590-1595 (2010). MSC: 82B03 33E20 45K05 PDFBibTeX XMLCite \textit{G. Pagnini} and \textit{F. Mainardi}, J. Comput. Appl. Math. 233, No. 6, 1590--1595 (2010; Zbl 1179.82008) Full Text: DOI arXiv
Gorenflo, Rudolf; Mainardi, Francesco Some recent advances in theory and simulation of fractional diffusion processes. (English) Zbl 1166.45004 J. Comput. Appl. Math. 229, No. 2, 400-415 (2009). MSC: 45K05 26A33 60G18 60G50 60G51 60J60 PDFBibTeX XMLCite \textit{R. Gorenflo} and \textit{F. Mainardi}, J. Comput. Appl. Math. 229, No. 2, 400--415 (2009; Zbl 1166.45004) Full Text: DOI arXiv
Mura, Antonio; Mainardi, Francesco A class of self-similar stochastic processes with stationary increments to model anomalous diffusion in physics. (English) Zbl 1173.26005 Integral Transforms Spec. Funct. 20, No. 3-4, 185-198 (2009). Reviewer: P. K. Banerji (Jodhpur) MSC: 26A33 33E12 33C60 44A10 60G18 PDFBibTeX XMLCite \textit{A. Mura} and \textit{F. Mainardi}, Integral Transforms Spec. Funct. 20, No. 3--4, 185--198 (2009; Zbl 1173.26005) Full Text: DOI arXiv
Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni; Gorenflo, Rudolf Time-fractional diffusion of distributed order. (English) Zbl 1229.35118 J. Vib. Control 14, No. 9-10, 1267-1290 (2008). MSC: 35K57 26A33 PDFBibTeX XMLCite \textit{F. Mainardi} et al., J. Vib. Control 14, No. 9--10, 1267--1290 (2008; Zbl 1229.35118) Full Text: DOI arXiv
Gorenflo, Rudolf; Mainardi, Francesco; Vivoli, Alessandro Continuous-time random walk and parametric subordination in fractional diffusion. (English) Zbl 1142.82363 Chaos Solitons Fractals 34, No. 1, 87-103 (2007). MSC: 82C41 82C70 PDFBibTeX XMLCite \textit{R. Gorenflo} et al., Chaos Solitons Fractals 34, No. 1, 87--103 (2007; Zbl 1142.82363) Full Text: DOI arXiv
Mainardi, Francesco; Mura, Antonio; Gorenfloh, Rudolf; Stojanović, Mirjana The two forms of fractional relaxation of distributed order. (English) Zbl 1165.26302 J. Vib. Control 13, No. 9-10, 1249-1268 (2007). MSC: 26A33 PDFBibTeX XMLCite \textit{F. Mainardi} et al., J. Vib. Control 13, No. 9--10, 1249--1268 (2007; Zbl 1165.26302) Full Text: DOI arXiv
Mainardi, Francesco; Pagnini, Gianni The role of the Fox-Wright functions in fractional sub-diffusion of distributed order. (English) Zbl 1120.35002 J. Comput. Appl. Math. 207, No. 2, 245-257 (2007). MSC: 35A08 35A22 26A33 33E12 33C45 33C60 44A10 45K05 PDFBibTeX XMLCite \textit{F. Mainardi} and \textit{G. Pagnini}, J. Comput. Appl. Math. 207, No. 2, 245--257 (2007; Zbl 1120.35002) Full Text: DOI arXiv
Mainardi, Francesco; Gorenflo, Rudolf; Vivoli, Alessandro Beyond the Poisson renewal process: a tutorial survey. (English) Zbl 1115.60082 J. Comput. Appl. Math. 205, No. 2, 725-735 (2007). MSC: 60K05 60K25 26A33 33E12 45K05 47G30 60G50 60G51 60G55 PDFBibTeX XMLCite \textit{F. Mainardi} et al., J. Comput. Appl. Math. 205, No. 2, 725--735 (2007; Zbl 1115.60082) Full Text: DOI
Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf Some aspects of fractional diffusion equations of single and distributed order. (English) Zbl 1122.26004 Appl. Math. Comput. 187, No. 1, 295-305 (2007). Reviewer: K. C. Gupta (Jaipur) MSC: 26A33 45K05 60G18 60J60 PDFBibTeX XMLCite \textit{F. Mainardi} et al., Appl. Math. Comput. 187, No. 1, 295--305 (2007; Zbl 1122.26004) Full Text: DOI arXiv
Mainardi, F.; Pagnini, G.; Gorenflo, R. Mellin convolution for subordinated stable processes. (English) Zbl 1411.60026 J. Math. Sci., New York 132, No. 5, 637-642 (2006). MSC: 60E07 60E10 PDFBibTeX XMLCite \textit{F. Mainardi} et al., J. Math. Sci., New York 132, No. 5, 637--642 (2006; Zbl 1411.60026) Full Text: DOI
Gorenflo, R.; Vivoli, A.; Mainardi, F. Discrete and continuous random walk models for space-time fractional diffusion. (English) Zbl 1411.60052 J. Math. Sci., New York 132, No. 5, 614-628 (2006). MSC: 60G15 60G50 60J27 PDFBibTeX XMLCite \textit{R. Gorenflo} et al., J. Math. Sci., New York 132, No. 5, 614--628 (2006; Zbl 1411.60052) Full Text: DOI
Mainardi, Francesco; Pagnini, Gianni; Saxena, R. K. Fox \(H\) functions in fractional diffusion. (English) Zbl 1061.33012 J. Comput. Appl. Math. 178, No. 1-2, 321-331 (2005). MSC: 33C60 33C20 33E12 33E20 33E30 26A33 44A15 60G18 60J60 PDFBibTeX XMLCite \textit{F. Mainardi} et al., J. Comput. Appl. Math. 178, No. 1--2, 321--331 (2005; Zbl 1061.33012) Full Text: DOI
Gorenflo, Rudolf; Vivoli, Alessandro; Mainardi, Francesco Discrete and continuous random walk models for space-time fractional diffusion. (English) Zbl 1125.76067 Nonlinear Dyn. 38, No. 1-4, 101-116 (2004). Reviewer: Gheorghe Oprişan (Bucureşti) MSC: 76R50 76M35 60J60 PDFBibTeX XMLCite \textit{R. Gorenflo} et al., Nonlinear Dyn. 38, No. 1--4, 101--116 (2004; Zbl 1125.76067) Full Text: DOI
Mainardi, Francesco Applications of integral transforms in fractional diffusion processes. (English) Zbl 1093.45003 Integral Transforms Spec. Funct. 15, No. 6, 477-484 (2004). Reviewer: Neville Ford (Chester) MSC: 45K05 44A10 26A33 33E12 42A38 35A22 60J60 35K05 PDFBibTeX XMLCite \textit{F. Mainardi}, Integral Transforms Spec. Funct. 15, No. 6, 477--484 (2004; Zbl 1093.45003) Full Text: DOI arXiv
Mainardi, Francesco; Pagnini, Gianni The Wright functions as solutions of the time-fractional diffusion equation. (English) Zbl 1053.35008 Appl. Math. Comput. 141, No. 1, 51-62 (2003). Reviewer: Ismail Taqi Ali (Safat) MSC: 35A22 26A33 35S10 PDFBibTeX XMLCite \textit{F. Mainardi} and \textit{G. Pagnini}, Appl. Math. Comput. 141, No. 1, 51--62 (2003; Zbl 1053.35008) Full Text: DOI
Mainardi, Francesco; Pagnini, Gianni Salvatore Pincherle: the pioneer of the Mellin-Barnes integrals. (English) Zbl 1050.33018 J. Comput. Appl. Math. 153, No. 1-2, 331-342 (2003). Reviewer: Robert G. Buschman (Langlois) MSC: 33E30 33C20 33C60 01-XX PDFBibTeX XMLCite \textit{F. Mainardi} and \textit{G. Pagnini}, J. Comput. Appl. Math. 153, No. 1--2, 331--342 (2003; Zbl 1050.33018) Full Text: DOI arXiv
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo Fractional diffusion: probability distributions and random walk models. (English) Zbl 0986.82037 Physica A 305, No. 1-2, 106-112 (2002). MSC: 82B41 76R50 60G50 35K57 PDFBibTeX XMLCite \textit{R. Gorenflo} et al., Physica A 305, No. 1--2, 106--112 (2002; Zbl 0986.82037) Full Text: DOI
Mainardi, Francesco; Gorenflo, Rudolf On Mittag-Leffler-type functions in fractional evolution processes. (English) Zbl 0970.45005 J. Comput. Appl. Math. 118, No. 1-2, 283-299 (2000). Reviewer: Ismail Taqi Ali (Safat) MSC: 45J05 26A33 33E20 PDFBibTeX XMLCite \textit{F. Mainardi} and \textit{R. Gorenflo}, J. Comput. Appl. Math. 118, No. 1--2, 283--299 (2000; Zbl 0970.45005) Full Text: DOI