Maximum Principles for a Class of Generalized Time-Fractional Diffusion Equations

citation_journal_title=Fract. Calc. Appl. Anal.; citation_title=Maximum principle for the fractional diffusion equations with the Riemann-Liouville fractional derivative and its applications; citation_author=M Al-Refai, Y Luchko; citation_volume=17; citation_issue=2; citation_publication_date=2014; citation_pages=483-498; citation_doi=10.2478/s13540-014-0181-5; citation_id=CR1 citation_journal_title=Appl. Math. Comput.; citation_title=Maximum principle for the multi-term time-fractional diffusion equations with the Riemann-Liouville fractional derivatives; citation_author=M Al-Refai, Y Luchko; citation_volume=257; citation_publication_date=2015; citation_pages=40-51; citation_id=CR2 citation_journal_title=Appl. Math. Lett.; citation_title=Maximum principle and its application for the nonlinear time-fractional diffusion equations with Cauchy-Dirichlet conditions; citation_author=M Borikhanov, M Kirane, BT Torebek; citation_volume=81; citation_publication_date=2018; citation_pages=14-20; citation_doi=10.1016/j.aml.2018.01.012; citation_id=CR3 citation_journal_title=J. Nonlinear Sci. Appl.; citation_title=Maximum principles for time-fractional Caputo-Katugampola diffusion equations; citation_author=L Cao, H Kong, SD Zeng; citation_volume=10; citation_publication_date=2017; citation_pages=2257-2267; citation_doi=10.22436/jnsa.010.04.75; citation_id=CR4 citation_title=Theory and Applications of Fractional Differential Equations, in: North–Holland Mathematics Studies; citation_publication_date=2006; citation_id=CR5; citation_author=AA Kilbas; citation_author=HM Srivastava; citation_author=JJ Trujillo; citation_publisher=Elsevier Science B.V. citation_journal_title=Fract. Calc. Appl. Anal.; citation_title=Extremum principle for the Hadamard derivatives and its application to nonlinear fractional partial differential equations; citation_author=M Kirane, BT Torebek; citation_volume=22; citation_issue=2; citation_publication_date=2019; citation_pages=358-378; citation_doi=10.1515/fca-2019-0022; citation_id=CR6 citation_journal_title=SIAM J. on Control and Optimization; citation_title=Approximate controllability of fractional evolution systems with Riemann–Liouville fractional derivatives; citation_author=ZH Liu, X Li; citation_volume=53; citation_issue=4; citation_publication_date=2015; citation_pages=1920-1933; citation_doi=10.1137/120903853; citation_id=CR7 citation_journal_title=Fract. Calc. Appl. Anal.; citation_title=Maximum principles for multi term space-time variable-order fractional diffusion equations and their applications; citation_author=ZH Liu, SD Zeng, YR Bai; citation_volume=19; citation_issue=1; citation_publication_date=2016; citation_pages=188-211; citation_doi=10.1515/fca-2016-0011; citation_id=CR8 citation_journal_title=J. Math. Anal. Appl.; citation_title=Maximum principle for the generalized time-fractional diffusion equation; citation_author=Y Luchko; citation_volume=351; citation_issue=1; citation_publication_date=2009; citation_pages=218-223; citation_doi=10.1016/j.jmaa.2008.10.018; citation_id=CR9 citation_journal_title=Computers Math. Appl.; citation_title=Some uniqueness and existence results for the initial boundary value problems for the generalized time-fractional diffusion equation; citation_author=Y Luchko; citation_volume=59; citation_issue=5; citation_publication_date=2010; citation_pages=1766-1772; citation_doi=10.1016/j.camwa.2009.08.015; citation_id=CR10 citation_journal_title=Fract. Calc. Appl. Anal.; citation_title=Maximum principle and its application for the time-fractional diffusion equations; citation_author=Y Luchko; citation_volume=14; citation_issue=1; citation_publication_date=2011; citation_pages=110-124; citation_doi=10.2478/s13540-011-0008-6; citation_id=CR11 citation_journal_title=Fract. Calc. Appl. Anal.; citation_title=On the maximum principle for a time-fractional diffusion equation; citation_author=Y Luchko, M Yamamoto; citation_volume=20; citation_issue=5; citation_publication_date=2017; citation_pages=1131-1145; citation_doi=10.1515/fca-2017-0060; citation_id=CR12 citation_journal_title=Handbook of Fractional Calculus with Applications; citation_title=Maximum principle for the time-fractional PDEs; citation_author=Y Luchko, M Yamamoto, A Kochubei, Y Luchko; citation_volume=2; citation_publication_date=2019; citation_pages=299-326; citation_id=CR13 L. Ma, C.P. Li, On Hadamard fractional calculus. Fractals 25, No 3 (2017), ID: 1750033. L. Ma, C.P. Li, On linite part integrals and Hadamard-type fractional derivatives. J. Comput. Nonlinear Dynam. 13, No 9 (2018), ID: 090905. citation_journal_title=Acta Math. Scientia; citation_title=Mixed variational inequalities driven by fractional evolutionary equations; citation_author=S Migórski, SD Zeng; citation_volume=39; citation_issue=2; citation_publication_date=2019; citation_pages=461-468; citation_doi=10.1007/s10473-019-0211-9; citation_id=CR16 citation_journal_title=Appl. Math. Lett.; citation_title=Maximum principles for fractional differential equations derived from Mittag Leffler functions; citation_author=JJ Nieto; citation_volume=23; citation_issue=10; citation_publication_date=2010; citation_pages=1248-1251; citation_doi=10.1016/j.aml.2010.06.007; citation_id=CR17 citation_title=Fractional Differential Equations; citation_publication_date=1999; citation_id=CR18; citation_author=I Podlubny; citation_publisher=Academic Press citation_title=Fractional Integrals and Derivatives: Theory and Applications; citation_publication_date=1993; citation_id=CR19; citation_author=SG Samko; citation_author=AA Kilbas; citation_author=OI Marichev; citation_publisher=Gordon and Breach citation_journal_title=Integral Transforms and Special Functions; citation_title=Integration and differentiation to a variable fractional order; citation_author=SG Samko, B Ross; citation_volume=1; citation_issue=4; citation_publication_date=1993; citation_pages=277-300; citation_doi=10.1080/10652469308819027; citation_id=CR20 citation_journal_title=Appl. Math. Comput.; citation_title=Maximum principle and numerical method for the multi-term time-space Riesz-Caputo fractional differential equations; citation_author=H Ye, F Liu, V Anh, I Turner; citation_volume=227; citation_publication_date=2014; citation_pages=531-540; citation_id=CR21 C.T. Yin, L. Ma, C.P. Li, Comparison principles for Hadamard-type fractional differential equations. Fractals 26, No 4 (2018), ID: 1850056. citation_journal_title=Z. Angew. Math. Phys.; citation_title=A class of fractional differential hemivariational inequalities with application to contact problem; citation_author=SD Zeng, ZH Liu, S Migórski; citation_volume=69; citation_issue=2; citation_publication_date=2018; citation_pages=36; citation_doi=10.1007/s00033-018-0929-6; citation_id=CR23 citation_journal_title=Commun. Nonlinear Sci.; citation_title=A class of time-fractional hemivariational inequalities with application to frictional contact problem; citation_author=SD Zeng, S Migórski; citation_volume=56; citation_publication_date=2018; citation_pages=34-48; citation_doi=10.1016/j.cnsns.2017.07.016; citation_id=CR24