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The critical exponent for an ordinary fractional differential problem. (English) Zbl 1189.34013
Summary: We consider the Cauchy problem for an ordinary fractional differential inequality with a polynomial nonlinearity with variable coefficient. A nonexistence result is proved and the critical exponent separating existence from nonexistence is found. This is proved in the absence of any regularity assumptions.

34A08Fractional differential equations
26A33Fractional derivatives and integrals (real functions)
45J05Integro-ordinary differential equations
Full Text: DOI
[1] R.P. Agarwal, M. Benchohra, S. Hamani, A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions, Acta Appl. Math., Available online · Zbl 1198.26004 · doi:10.1007/s10440-008-9356-6
[2] Furati, K. M.; Tatar, N. -E.: An existence result for a nonlocal fractional differential problem, J. fract. Calc. 26, 43-51 (2004) · Zbl 1101.34001
[3] Furati, K. M.; Tatar, N. -E.: Behavior of solutions for a weighted Cauchy-type fractional differential problem, J. fract. Calc. 28, 23-42 (2005) · Zbl 1131.26304
[4] Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J.: Theory and applications of fractional differential equations, North-holland mathematics studies 204 (2006) · Zbl 1092.45003
[5] Kilbas, A. A.; Trujillo, J. J.: Differential equations of fractional order: methods, results and problems I, Appl. anal. 78, No. 1--2, 153-192 (2001) · Zbl 1031.34002 · doi:10.1080/00036810108840931
[6] Kilbas, A. A.; Trujillo, J. J.: Differential equations of fractional order: methods, results and problems II, Appl. anal. 81, No. 2, 435-493 (2001) · Zbl 1033.34007 · doi:10.1080/0003681021000022032
[7] Samko, S. G.; Kilbas, A. A.; Marichev, O. I.: Fractional integrals and derivatives: theory and applications, (1993) · Zbl 0818.26003
[8] Kirane, M.; Laskri, Y.; Tatar, N. -E.: Critical exponents of Fujita type for certain evolution equations and systems with spatio-temporal fractional derivatives, J. math. Anal. appl. 312, No. 2, 488-501 (2005) · Zbl 1135.35350 · doi:10.1016/j.jmaa.2005.03.054
[9] Kirane, M.; Tatar, N. -E.: Nonexistence of solutions to a hyperbolic equation with a time fractional damping, Z. anal. Anwendungen 25, 131-142 (2006) · Zbl 1106.26009 · doi:10.4171/ZAA/1281
[10] Kirane, M.; Tatar, N. -E.: Absence of local and global solutions to an elliptic system with time-fractional dynamical boundary conditions, Siberian J. Math. 48, No. 3, 477-488 (2007) · Zbl 1164.35352 · emis:journals/SMZ/2007/03/593.htm
[11] Kirane, M.; Tatar, N. -E.: Nonexistence for the Laplace equation with a dynamical boundary condition of fractional type, Siberian math. J. 48, No. 5, 849-856 (2007) · Zbl 1164.35360 · emis:journals/SMZ/2007/05/1056.html
[12] Tatar, N. -E.: A wave equation with fractional damping, Z. anal. Anwendungen 22, No. 3, 609-617 (2003) · Zbl 1059.35084 · doi:10.4171/ZAA/1165
[13] Mitidieri, E.; Pohozaev, S.: A priori estimates and blow-up of solutions to nonlinear partial differential equations and inequalities, Proc. Steklov inst. Math. 234, 1-383 (2001) · Zbl 0987.35002
[14] Podlubny, I.: Fractional differential equations, Math. in sci. And eng. 198 (1999) · Zbl 0924.34008