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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 한국전산응용수학회 Journal of applied mathematics & informatics Journal of applied mathematics & informatics 제33권 제5호
- 발행연도
- 2015.1
- 수록면
- 699 - 721 (23page)
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This paper investigates the existence of mild solution for a fractional integro-differential equations with a deviating argument and nonlocal initial condition in an arbitrary separable Hilbert space H via technique of approximations. We obtain an associated integral equation and then consider a sequence of approximate integral equations obtained by the projection of considered associated nonlocal fractional integral equation onto finite dimensional space. The existence and uniqueness of solutions to each approximate integral equation is obtained by virtue of the analytic semigroup theory via Banach fixed point theorem. Next we demonstrate the convergence of the solutions of the approximate integral equations to the solution of the associated integral equation. We consider the Faedo-Galerkin approximation of the solution and demonstrate some convergenceresults. An example is also given to illustrate the abstract theory.
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참고문헌 (36)
참고문헌 신청
K.S. Miller / 1993 / An Introduction to the Fractional Calculus and Fractional Differential Equations. / John Wiley and Sons, Inc
S.G. Samko / 1993 / Fractional Integrals and Derivatives: Theory and Applications / Gordon and Breach Science Publishe
I. Podlubny. / 1999 / Fractional Differential Equations, Mathematics in Science and Engineering, Vol. 198 / Academic Press
A. A. Kilbas. / 2006 / Theory and Applications of Fractional Differential Equations / Elsevier
M. El-Borai / 2002 / Some probability densities and fundamental solutions of fractional evolution equations / Chaos Solitons Fractals 14:433~440
S.G. Samko / 1993 / Fractional Integrals and Derivatives: Theory and Applications / Gordon and Breach Science Publishe
I. Podlubny. / 1999 / Fractional Differential Equations, Mathematics in Science and Engineering, Vol. 198 / Academic Press
A. A. Kilbas. / 2006 / Theory and Applications of Fractional Differential Equations / Elsevier
M. El-Borai / 2002 / Some probability densities and fundamental solutions of fractional evolution equations / Chaos Solitons Fractals 14:433~440
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