General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems

References

1 Al-Refai M. Luchko Yu. Maximum principles for the fractional diffusion equations with the Riemann-Liouville fractional derivative and their applications Fract. Calc. Appl. Anal 17 No 2 2014 483 498 DOI: 10.2478/s13540-014-0181-5;Suche in Google Scholar

2 Chechkin A.V. Gorenflo R. Sokolov I.M. Fractional diffusion in inhomogeneous media J. Phys. A, Math. Gen. 38 2005 679 68410.1088/0305-4470/38/42/L03Suche in Google Scholar

3 Chechkin A.V. Gorenflo R. Sokolov I.M. Gonchar V.Yu. Distributed order time fractional diffusion equation Fract. Calc. Appl. Anal. 6 2003 259 279Suche in Google Scholar

4 Chechkin A.V. Gorenflo R. Sokolov I.M. Retarding subdiffusion and accelerating superdiffusion governed by distributed order fractional diffusion equations Phys. Rev. E 66 2002 1 710.1103/PhysRevE.66.046129Suche in Google Scholar PubMed

5 Daftardar-Gejji V. Bhalekar S. Boundary value problems for multi-term fractional differential equations J. Math. Anal. Appl. 345 2008 754 76510.1016/j.jmaa.2008.04.065Suche in Google Scholar

6 Feller W. An Introduction to Probability Theory and its Applications Vol. 2 Wiley New York 1966Suche in Google Scholar

7 Jiang H. Liu F. Turner I.W. Burrage K. Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain Computers and Math. with Appl. 64 2012 3377 338810.1016/j.camwa.2012.02.042Suche in Google Scholar

8 Kochubei A.N. General fractional calculus, evolution equations, and renewal processes Integr. Equa. Operator Theory 71 2011 583 60010.1007/s00020-011-1918-8Suche in Google Scholar

9 Kochubei A.N. Distributed order calculus and equations of ultraslow diffusion J. Math. Anal. Appl. 340 2008 252 28110.1016/j.jmaa.2007.08.024Suche in Google Scholar

10 Li Z. Liu Y. Yamamoto M. Initial-boundary value problems for multi-term time-fractional diffusion equations with positive constant coefficients Appl. Math. and Computation 257 2015 381 39710.1016/j.amc.2014.11.073Suche in Google Scholar

11 Li Z. Luchko Yu. Yamamoto M. Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations Fract. Calc. Appl. Anal. 17 No 4 2014 1114 1136 DOI: 10.2478/s13540-014-0217-x;Suche in Google Scholar

12 Luchko Yu. Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation Fract. Calc. Appl. Anal. 15 No 1 2012 141 160 DOI: 10.2478/s13540-012-0010-7;Suche in Google Scholar

13 Luchko Yu. Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation J. Math. Anal. Appl. 374 2011 538 54810.1016/j.jmaa.2010.08.048Suche in Google Scholar

14 Luchko Yu. Some uniqueness and existence results for the initial-boundary value problems for the generalized time-fractional diffusion equation Comput. Math. Appl. 59 No 5 2010 1766 177210.1016/j.camwa.2009.08.015Suche in Google Scholar

15 Luchko Yu. Maximum principle for the generalized time-fractional diffusion equation J. Math. Anal. Appl. 351 No 1 2009 218 22310.1016/j.jmaa.2008.10.018Suche in Google Scholar

16 Luchko Yu. Boundary value problems for the generalized time-fractional diffusion equation of distributed order Fract. Calc. Appl. Anal. 12 2009 409 422Suche in Google Scholar

17 Luchko Yu. Operational method in fractional calculus Fract. Calc. Appl. Anal. 2 1999 463 489Suche in Google Scholar

18 Luchko Yu. Gorenflo R. An operational method for solving fractional differential equations with the Caputo derivatives Acta Math. Vietnam. 24 No 2 1999 207 233Suche in Google Scholar

19 Meerschaert M.M. Scheffler H.-P. Stochastic model for ultraslow diffusion Stochastic Process. Appl. 116 2006 1215 123510.1016/j.spa.2006.01.006Suche in Google Scholar

20 Metzler R. Jeon J.-H. Cherstvy A. G. Barkai E. Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking Phys. Chem. Chem. Phys. 16 20142412810.1039/C4CP03465ASuche in Google Scholar

21 Naber M. Distributed order fractional subdiffusion Fractals 12 2004 23 3210.1142/S0218348X04002410Suche in Google Scholar

22 Protter M.H. Weinberger H.F. Maximum Principles in Differential Equations Springer Berlin 1999Suche in Google Scholar

23 Sakamoto K. Yamamoto M. Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems J. Math. Anal. Appl. 382 No 1 2011 426 44710.1016/j.jmaa.2011.04.058Suche in Google Scholar

24 Samko S.G. Kilbas A.A. Marichev O.I. Fractional Integrals and Derivatives: Theory and Applications Gordon and Breach Yverdon 1993Suche in Google Scholar

25 Schilling R.L. Song R. Vondracek Z. Bernstein Functions. Theory and Application De Gruyter Berlin 201010.1515/9783110215311Suche in Google Scholar

26 Schneider W.R. Wyss W. Fractional diffusion and wave equations J. Math. Phys. 30 1989 134 14410.1063/1.528578Suche in Google Scholar

27 Sokolov I.M. Chechkin A.V. Klafter J. Distributed-order fractional kinetics Acta Phys. Polon. B 35 2004 1323 1341Suche in Google Scholar

28 Suzuki A. Niibori Y. Fomin S.A. Chugunov V.A. Hashida T. Prediction of reinejction effects in fault-related subsidiary structures by using fractional derivative-based mathematical models for sustainable design of geothermal reservoirs Geothermics 57 2015 196 20410.1016/j.geothermics.2015.04.001Suche in Google Scholar

29 Suzuki A. Niibori Y. Fomin S.A. Chugunov V.A. Hashida T. Analysis of water injection in fractured reservoirs using a fractional-derivative-based mass and heat transfer model Mathematical Geosciences 47 2014 31 4910.1007/s11004-014-9522-5Suche in Google Scholar

30 Umarov S. Gorenflo R. Cauchy and nonlocal multi-point problems for distributed order pseudo-differential equations Z. Anal. Anwend. 24 2005 449 46610.4171/ZAA/1250Suche in Google Scholar

31 Vladimirov V.S. Equations of Mathematical Physics Nauka Moscow 197110.1063/1.3022385Suche in Google Scholar

32 Walter W. On the strong maximum principle for parabolic differential equations Proc. Edinb. Math. Soc. 29 1986 93 9610.1017/S0013091500017442Suche in Google Scholar