• The Pure and Applied Mathematics
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• v.20 no.3
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• pp.159-180
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• 2013

We establish a common fixed point theorem for mappings under ${\phi}$-contractive conditions on intuitionistic fuzzy metric spaces. As an application of our result we study the existence and uniqueness of the solution to a nonlinear Fredholm integral equation. We also give an example to validate our result.

• Korean Journal of Mathematics
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• v.29 no.4
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• pp.749-763
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• 2021

This research article deals with the Mittag-Leffler-Hyers-Ulam stability of linear and impulsive fractional order differential equation which involves the Caputo derivative. The application of the generalized fractional Fourier transform method and fixed point theorem, evaluates the existence, uniqueness and stability of solution that are acquired for the proposed non-linear problems on Lizorkin space. Finally, examples are introduced to validate the outcomes of main result.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.439-447
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• 2017

This paper investigates the inverse problem of determining an unknown heat radiative coefficient, which is only time-dependent. This is an ill-posed problem, that is, small errors in data may cause huge deviations in determining solution. In this paper, the existence and uniqueness of the problem is established by the second Volterra integral equation theory, and the method of trace-type functional formulation combined with finite difference scheme is studied. One typical numerical example using the proposed method is illustrated and discussed.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.65-77
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• 2013

In this paper, we develop the operational Tau method for solving nonlinear Volterra integro-differential equations of the second kind. The existence and uniqueness of the problem is provided. Here, we show that the nonlinear system resulted from the operational Tau method has a semi triangular form, so it can be solved easily by the forward substitution method. Finally, the accuracy of the method is verified by presenting some numerical computations.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.365-375
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• 2015

Of concern is the existence, uniqueness, and continuous dependence of a mild solution of a nonlocal Cauchy problem for a semilinear mixed Volterra-Fredholm functional integrodifferential equation. Our analysis is based on the theory of a strongly continuous semigroup of operators and the Banach fixed point theorem.

• Journal of the Korean Mathematical Society
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• v.42 no.1
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• pp.153-169
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• 2005

A fuzzy stochastic differential equation contains a fuzzy valued diffusion term which is defined by stochastic integral of a fuzzy process with respect to 1-dimensional Brownian motion. We prove the existence and uniqueness of the solution for fuzzy stochastic differential equation under suitable Lipschitz condition. To do this we prove and use the maximal inequality for fuzzy stochastic integrals. The results are illustrated by an example.

• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.561-569
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• 2002

In this paper we prove the existence and uniqueness of a mild solution of a functional differential equation of Sobolev type with nonlocal condition using the semigroup theory and the Banach fixed point principle.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.337-345
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• 2004

In allelic model X = ($\chi_1\chi$_2ㆍㆍㆍ, \chi_d$), M_f(t) = f(p(t)) - ${{\int^t}_0}\;Lf(p(t))ds$ is a P-martingale for diffusion operator L under the certain conditions. In this note, we can show existence and uniqueness of solution for stochastic differential equation and martingale problem associated with mean vector. Also, we examine that if the operator related to this martingale problem is connected with Markov processes under certain circumstance, then this operator must satisfy the maximum principle.

• East Asian mathematical journal
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• v.26 no.1
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• pp.95-103
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• 2010

In this paper using Lipschitz continuity of the resolvent operator associated with general H-maximal m-relaxed $\eta$-monotone operators, existence and uniqueness of the solution of a variational inclusion system is proved. Also, an iterative algorithm and its convergence analysis is given.

• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.615-640
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• 2022

In this paper, we investigate a time-dependent double obstacle problem associated with the model of European call option pricing with transaction costs. We prove the existence and uniqueness of a W^2,1_p,loc solution to the problem. We then characterize the behavior of the free boundaries in terms of continuity and values of limit points.