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Henry-Gronwall type retarded integral inequalities and their applications to fractional differential equations with delay. (English) Zbl 1247.26043
Summary: This paper presents retarded integral inequalities of Henry-Gronwall type. Applying these inequalities, we study certain properties of solutions of fractional differential equations with delay.

26D15Inequalities for sums, series and integrals of real functions
Full Text: DOI
[1] Agarwal, R. P.; Deng, S.; Zhang, W.: Generalization of a retarded Gronwall-like inequality and its applications, Appl. math. Comput. 165, 599-612 (2005) · Zbl 1078.26010 · doi:10.1016/j.amc.2004.04.067
[2] Denton, Z.; Vatsala, A. S.: Fractional integral inequalities and applications, Comput. math. Appl. 59, 1087-1094 (2010) · Zbl 1189.26044 · doi:10.1016/j.camwa.2009.05.012
[3] Ei-Owaidy, H.; Ragab, A.; Abdeldaim, A.: On some new integral inequalities of Gronwall -- Bellman type, Appl. math. Comput. 106, 289-303 (1999) · Zbl 1037.26011 · doi:10.1016/S0096-3003(98)10131-5
[4] Henry, D.: Geometric theory of semilinear parabolic equations, (1981) · Zbl 0456.35001
[5] Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J.: Theory and applications of fractional differential equations, Theory and applications of fractional differential equations 204 (2006) · Zbl 1092.45003
[6] Kuczma, M.: An introduction to the theory of functional equations and inequalities: Cauchy’s equation and Jensen’s inequality, (2009) · Zbl 1221.39041
[7] Lipovan, O.: A retarded Gronwall-like inequality and its applications, J. math. Anal. appl. 252, 389-401 (2000) · Zbl 0974.26007 · doi:10.1006/jmaa.2000.7085
[8] Ma, Q.; Pec&breve, J.; Arić: Some new explicit bounds for weakly singular integral inequalities with applications to fractional differential and integral equations, J. math. Anal. appl. 341, 894-905 (2008) · Zbl 1142.26015
[9] Medved&breve, M.; : A new approach to an analysis of henry type integral inequalities and their bihari type versions, J. math. Anal. appl. 214, 349-366 (1997) · Zbl 0893.26006
[10] Medved&breve, M.; : Integral inequalities and global solutions of semilinear evolution equations, J. math. Anal. appl. 267, 643-650 (2002)
[11] Pachpatte, B. G.: On some generalizations of Bellman’s lemma, J. math. Anal. appl. 5, 141-150 (1975) · Zbl 0305.26010 · doi:10.1016/0022-247X(75)90146-8
[12] Pachpatte, B. G.: Inequalities for differential and integral equations, (1998) · Zbl 1032.26008
[13] Pachpatte, B. G.: Explicit bounds on certain integral inequalities, J. math. Anal. appl. 267, 48-61 (2002) · Zbl 0996.26008 · doi:10.1006/jmaa.2001.7743
[14] Pachpatte, B. G.: Integral and finite difference inequalities and applications, (2006) · Zbl 1104.26015
[15] Podlubny, I.: Fractional differential equations, (1999) · Zbl 0924.34008
[16] Ye, H.; Ding, Y.; Gao, J.: The existence of a positive solution of D$\alpha [x(t) - x(0)]=x(t)f(t,xt)$, Positivity 11, 341-350 (2007) · Zbl 1121.34064 · doi:10.1007/s11117-006-2038-6
[17] Ye, H.; Gao, J.; Ding, Y.: A generalized Gronwall inequality and its application to a fractional differential equation, J. math. Anal. appl. 328, 1075-1081 (2007) · Zbl 1120.26003 · doi:10.1016/j.jmaa.2006.05.061