[PDF] Top 20 Some new nonlinear integral inequalities with weakly singular kernel and their applications to FDEs

... of some fractional differential equations, many inequalities with singular kernels have been developed (for example, see [–] and the references ...these inequalities, Medveď [] dis- cussed ... See full document

... a new method to solve integral in- equalities of Henry-Gronwall type, then he got the explicit bounds with a quite simple for- mula, similar to the classic Gronwall-Bellman ...a new weakly ... See full document

... of inequalities for a two-dimensional case, more attention has also been paid to weakly singular integral inequalities in two variables and their applications to the partial ... See full document

... generalized nonlinear weakly singular retarded Wendroff-type integral inequality with maxima of an unknown function of two ...for some known ...for some singular ... See full document

... Integral inequalities are used as handy tools in the study of the qualitative properties of solutions to differential and integral equations, such as existence, uniqueness, bounded- ness, stability, ... See full document

... various weakly singular inte- gral inequalities and their discrete analogues have attracted more and more attention and play a fundamental role in the study of the theory of singular ... See full document

... scalar weakly sin- gular integro-differential equation of the first ...a new equation comprising additional derivative terms and integro-differential terms with smooth kernel was ...this new ... See full document

... have to introduce novel techniques and results to overcome the difficult from the weakly singular kernels and nonlinear terms h and g. For example, the first important step is how to construct a ... See full document

... of nonlinear integral inequalities with the unknown function composed with a given function on the left hand side, more than one distinct nonlinear integrals on its right-hand side, and ... See full document

... Some new weakly singular integral inequalities of Wendroff type are established, which generalized some known weakly singular inequalities for ... See full document

... () In this section, based on the definition of Riemann-Liouville (R-L) and Erdélyi-Kober (E-K) fractional integral, we will study the boundedness of a certain FDE with R-L frac- tional operator and E-K fractional ... See full document

... Some nonlinear weakly singular integral inequalities in two variables which generalize some known results are ...equations, integral equations, and evolution ... See full document

... Integral inequalities play a dominant role in the study quantitative properties of solutions of differential and inte- gral ...famous inequalities of this type is known as “Gronwall’s inequality”, ... See full document

... Remark  For the case α =  () is the classical Hardy inequality. The almost  years of research until Hardy finally proved this inequality in  (see []) is described in detail in []. In particular, it is ... See full document

... reproducing kernel method (RKM) to solve fractional differential equations in reproducing kernel Hilbert ...series. Some numerical examples are studied to demonstrate the accuracy of the given ... See full document

... There is a large literature on nonlinear singular integral equations with Hiibert and Cauchy kernel and on related nonlinear Riemann-Hilbert problems for analytic functions, cf.. the mon[r] ... See full document

... of some fundamental integral inequalities used in the theory of differential and integral equations on time ...illustrate some time scale Pachpatte- type inequalities by ... See full document

... 3. Some applications of two-dimensional ...present some applications of the given inequalities to study the boundedness, stability and uniqueness solutions of certain nonlinear ... See full document

... Gronwall-type integral inequalities involving iter- ated integrals by replacing the unknown function u in the right-hand side of ...for some constant p. In , Agarwal et al. [] investigated ... See full document

... Remark 3.17. Using our main results in this paper, we can obtain many dynamic inequal- ities on some peculiar time scales. Due to limited space, their statements are omitted here. At the end of this paper, we ... See full document