Research ArticleOpen AccessGoogle Scholar indexed
Existence and Uniqueness of Solution for a Fractional Order Integro-Differential Equation with Non-Local and Global Boundary Conditions
- 1
- 2
- 3
Applied Mathematics·Volume 02 (2011)·Pages 1292–1296·Published 11 October 2011·DOI10.4236/am.2011.210179
Copy link · social · email
Abstract
In this paper, we prove an important existence and uniqueness theorem for a fractional order Fredholm – Volterra integro-differential equation with non-local and global boundary conditions by converting it to the corresponding well known Fredholm integral equation of second kind. The considered in this paper has been solved already numerically in [1].
KeywordsFractional Order Integro-Differential EquationNon-Local Boundary ConditionsFundamental Solution
- D. Nazari and S. Shahmorad, “Application of Fractional Differential Transform Method to the Fractional Order Integro-Differential Equations with Nonlocal Boundary Conditions,” Journal of Computational and Applied Ma-thematics, Vol. 234, No. 3, 2010, pp. 883-891. doi:10.1016/j.cam.2010.01.053
- S. G. Samko, A. A. Kilbas and O. I. Marichev, “Fractional Integrals and De-rivatives,” Theory and Applications, Cordon and Breach, Yverdon, 1993.
- C. J. Tranter, “Integral Transforms in Mathematical Physics,” London and New York, 1949.
- V. S. Vladimirov, “Equation of Mathematical Physics,” Mir Publication, Moscow, 1984.
- G. E. Shilov, “Mathematical Analysis. The Second Special Course,” Nauka, Moscow, 1965.
- S. M. Hosseini and N. A. Aliev, “Sufficient Conditions for the Reduction of a BVP for PDE with Non-Local and Global Boundary Conditions to Fredholm Integral Equations (on a Rectan-gular Domain),” Applied Mathematics and Computation, Vol. 147, No. 3, 2004, pp. 669-685.
- F. Bahrami, N. Aliev and S. M. Hosseini, “A Method for the Reduction of Four Imensional Mixed Problems with General Boundary Conditions to a System of Second Kind Fredholm Integral Equations,” Italian Journal of Pure and Applied Mathematics, No. 17, 2005, pp. 91-104.
- N. Aliev and M. Jahanshehi, “Solution of Poissoins Equation with Global, Local and Non-Local Boundary Conditions,” In-ternational Journal of Mathematical Education in Science and Technology, Vol. 33, No. 2, 2002, pp. 241-247. doi:10.1080/00207390110097551