Basics of Volterra integral equations on time scales

机译：时间尺度上Volterra积分方程的基础

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This paper studies existence and uniqueness of solutions to generalizedVolterra integral equations. Since our proof for existence and uniqueness doesnot make use of Banach fixed point theorem unlike the previous papers focusedon this subject, we can replace continuity property of the kernel function withthe weaker one rd-continuity. The paper also covers results concerning thefollowing concepts: The notion of resolvent kernel, and its role in formulationof the solution, the reciprocity property of kernels, Piccard iterates,relation between linear dynamic equations and Volterra integral equations, somespecial type of kernels together with several illustrative examples.

机译：本文研究了广义Volterra积分方程解的存在性和唯一性。因为我们的存在性和唯一性证明不像以前的论文那样利用Banach不动点定理，所以可以用较弱的一阶连续性代替核函数的连续性。本文还涵盖了有关以下概念的结果：可分解核的概念及其在解决方案中的作用，核的互易性，Piccard迭代，线性动力学方程和Volterra积分方程之间的关系，某些特殊类型的核以及一些说明性的例子例子。

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Karpuz, Basak;
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年度 2011
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正文语种 {"code":"en","name":"English","id":9}
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专利

1. Volterra Integral Equations on Time Scales: Basic Qualitative and Quantitative Results with Applications to Initial Value Problems on Unbounded Domains [J] . International Journal of Difference Equations . 2008,第1期

机译：Volterra时间尺度积分方程：基本定性和定量结果及其在无界域上的初值问题的应用
2. Volterra Integral Equations on Unbounded Time Scales [J] . Andrejs Reinfelds, Shraddha Christian International Journal of Difference Equations . 2019,第2期

机译：无界时间尺度上的Volterra积分方程
3. Qualitative analysis of nonlinear Volterra integral equations on time scales using resolvent and Lyapunov functionals [J] . Adivar Murat, Raffoul Youssef N. Applied mathematics and computation . 2016,第Null期

机译：使用分解函数和Lyapunov泛函在时间尺度上对非线性Volterra积分方程进行定性分析。
4. Numerical solution of stochastic mixed Volterra-Fredholm integral equations driven by space-time Brownian motion via two-dimensional block pulse functions [C] . Farkhondeh Hosseini Shekarabi, Tayebeh Damercheli International Conference on Analysis and Applied Mathematics . 2018

机译：天空时间褐色运动通过二维块脉冲函数驱动的随机混合Volterra-Fredholm积分方程的数值解
5. Me, Myself and I: Time-Inconsistent Stochastic Control, Contract Theory and Backward Stochastic Volterra Integral Equations [D] . Hernandez Ramirez, Miguel Camilo. 2021

机译：我，我自己和我：时间不一致的随机控制，合同理论和落后的随机Volterra积分方程
6. On some nonlinear retarded Volterra–Fredholm type integral inequalities on time scales and their applications [O] . Haidong Liu -1

机译：关于时标上的某些非线性延迟Volterra-Fredholm型积分不等式及其应用
7. Analysis of Perturbed Volterra Integral Equations on Time Scales [O] . Eleonora Messina, Youssef N. Raffoul, Antonia Vecchio 2020

机译：时间尺度扰动Volterra积分方程的分析

Basics of Volterra integral equations on time scales

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