On some new integral inequalities of Growall–Bellman type

Henry-Gronwall Integral Inequalities with “Maxima” and Their Applications to Fractional Differential Equations

“…where 1 and 1 are defined by (16) and (17), respectively. Applying Corollary 2 for (34) and (35), we obtain…”

“…Shao and Meng [11] studied a certain class of nonlinear inequalities of Gronwall-Bellman type, which is used to a qualitative analysis to certain fractional differential equations. For other results on the subject we refer to [12][13][14][15][16][17][18] and references cited therein.…”

On Some Gamidov Integral Inequalities On Time Scales and Applications

“…One of the best known and widely used is the so-called Gronwall-Bellman integral inequality. In view of its important applications, many and various generalizations, extensions, and variants have appeared in the literature, we can mention [1,4,5,6,8,9,10,11,13,14,15,16,17,18,19] and references cited therein.…”

On some Nonlinear Integral Inequalities for Volterra Integral Equations

“…In recent years nonlinear integral inequalities have received considerable attention because of the important applications to a variety of problems in diverse fields of nonlinear differential and integral equations. Basic inequalities are established by Gronwall [5], Bellman [3] and Pachpatte [8] provide explicit bounds on solutions of a class of differential and integral equations which are further studied by many mathematicians see [1,2,4,7,9,10].…”