• Journal of the Chungcheong Mathematical Society
• /
• v.28 no.2
• /
• pp.345-352
• /
• 2015

We study the existence of mild solutions of partial neutral integrodifferential equations with unbounded delay by using the fixed point criterion for condensing operators.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2008.04a
• /
• pp.26-28
• /
• 2008

This paper is to investigate the existence theorem for the semilinear fuzzy integrodifferential equation in ${E_N}$ by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in ${E_N}$. Main tool is successive iteration method.

• Kyungpook Mathematical Journal
• /
• v.53 no.1
• /
• pp.87-98
• /
• 2013

In this paper, we devoted to study the existence and uniqueness of nonlinear fuzzy neutral integrodifferential equations. Moreover we study the fuzzy solution for the normal, convex, upper semicontinuous, and compactly supported interval fuzzy number. The results are obtained by using the Banach fixed-point theorem. An example is provided to illustrate the theory.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.9 no.4
• /
• pp.339-342
• /
• 2009

In this paper, we investigate the existence and uniqueness of fuzzy solutions for semilinear fuzzy integrodifferential equations using integral contractor. The notion of 'bounded integral contractor', introduced by Altman[1], is weaker than Lipschitz condition.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.18 no.4
• /
• pp.543-548
• /
• 2008

This paper is to investigate the existence theorem for the semilinear fuzzy integrodifferential equation in $E_N$ by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in $E_N$. Main tool is successive iteration method.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.4
• /
• pp.793-809
• /
• 2021

This paper gives sufficient conditions to ensure the existence and stability of solutions for generalized nonlinear fractional integrodifferential equations of order α (1 < α < 2). The main theorem asserts the stability results in a weighted Banach space, employing the Krasnoselskii's fixed point technique and the existence of at least one mild solution satisfying the asymptotic stability condition. Two examples are provided to illustrate the theory.

• Journal of the Korean Mathematical Society
• /
• v.56 no.1
• /
• pp.149-167
• /
• 2019

In this work, we study the existence, uniqueness and stability in the ${\alpha}$-norm of solutions for some stochastic partial functional integrodifferential equations. We suppose that the linear part has an analytic resolvent operator in the sense given in Grimmer [8] and the nonlinear part satisfies a $H{\ddot{o}}lder$ type condition with respect to the ${\alpha}$-norm associated to the linear part. Firstly, we study the existence of the mild solutions. Secondly, we study the exponential stability in pth moment (p > 2). Our results are illustrated by an example. This work extends many previous results on stochastic partial functional differential equations.

• Proceedings of the KSME Conference
• /
• 2008.11a
• /
• pp.121-126
• /
• 2008

A plane strain problem of a crack on interface between an isotropic elastic conductor and a transversely isotropic piezoelectric ceramics is considered. The problem is reduced to system integrodifferential equations on the interface. These equations relate the normal and tangential components of the crack opening vector with distribution of normal and shear stresses on the crack surfaces. It therefore make it possible to obtain an exact solution as a function of the loading applied to the crack surfaces. As an example, some analytical solutions of the crack problem are given.

• East Asian mathematical journal
• /
• v.19 no.1
• /
• pp.91-102
• /
• 2003

In this paper we prove the existence of mild and strong solutions of nonlinear delay integrodifferential equations with nonlocal conditions. The results are obtained by using the Schauder fixed point theorem and resolvent operator.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.7 no.2
• /
• pp.35-49
• /
• 2003

In this paper, finite volume element methods for nonlinear parabolic integrodifferential problems are proposed and analyzed. The optimal error estimates in $L^p\;and\;W^{1,p}\;(2\;{\leq}\;p\;{\leq}\;{\infty})$ as well as some superconvergence estimates in $W^{1,p}\;(2\;{\leq}\;p\;{\leq}\;{\infty})$ are obtained. The main results in this paper perfect the theory of FVE methods.