Nonlinear Gronwall–Bellman Type Inequalities and Their Applications

نویسندگان

  • Weimin Wang
  • Yuqiang Feng
  • Yuanyuan Wang
  • Hari M. Srivastava
چکیده

In this paper, some nonlinear Gronwall–Bellman type inequalities are established. Then, the obtained results are applied to study the Hyers–Ulam stability of a fractional differential equation and the boundedness of solutions to an integral equation, respectively.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Advanced Gronwall-Bellman-Type Integral Inequalities and Their Applications

In this paper, some new nonlinear generalized Gronwall-Bellman-Type integral inequalities with mixed time delays are established. These inequalities can be used as handy tools to research stability problems of delayed differential and integral dynamic systems. As applications, based on these new established inequalities, some p-stable results of a integro-differential equation are also given. T...

متن کامل

Some New Nonlinear Integro-differential Inequalities of Gronwall-bellman-pachpatte Type

In this paper we establish some new nonlinear integro-differential inequalities of Gronwall-Bellman-Pachpatte type for function of one independent variable. The purpose of this paper is to extend certain results which proved by Pachpatte in [On some fundamental integrodifferential and integral inequalities, An. Sti. Univ. Al. I. Cuza, Iasi, Vol.23 (1977), 77-86]. The inequalities obtained here ...

متن کامل

Nonlinear Retarded Integral Inequalities of Gronwall–bellman Type and Applications

The aim of this paper is to establish some new nonlinear retarded integral inequalities of Gronwall-Bellman type. More accurately we extend certain results which have been proved in El-Owaidy et. al, [12] and Abdeldaim and Yakout [2] to some nonlinear retarded integral inequalities. We also give some applications to estimate the solutions of some nonlinear retarded differential equations to ill...

متن کامل

Generalized Gronwall-Bellman-type discrete inequalities and their applications

* Correspondence: [email protected] School of Science, Shandong University of Technology, Zibo, 255049 Shandong, China Full list of author information is available at the end of the article Abstract In this paper, some new nonlinear Gronwall-Bellman-type discrete inequalities are established, which can be used as a handy tool in the research of qualitative and quantitative properties of solutions ...

متن کامل

On Some New Retarded Nonlinear Integral Inequalities and Their Applications

In this paper we present some new generalized retarded nonlinear integral inequalities of Gronwall-Bellman type. Using integral and differential skills, some new results which provide explicit bounds on unknown functions in integral inequalities are investigated. Some applications are also presented to illustrate the usefulness of some of our results.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2017