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Existence and Uniqueness of Solution for a Fractional Order Integro-Differential Equation with Non-Local and Global Boundary Conditions

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DOI: 10.4236/am.2011.210179    4,733 Downloads   8,803 Views   Citations

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].

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

M. Fatemi, N. Aliev and S. Shahmorad, "Existence and Uniqueness of Solution for a Fractional Order Integro-Differential Equation with Non-Local and Global Boundary Conditions," Applied Mathematics, Vol. 2 No. 10, 2011, pp. 1292-1296. doi: 10.4236/am.2011.210179.

References

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[2] S. G. Samko, A. A. Kilbas and O. I. Marichev, “Fractional Integrals and De-rivatives,” Theory and Applications, Cordon and Breach, Yverdon, 1993.
[3] C. J. Tranter, “Integral Transforms in Mathematical Physics,” London and New York, 1949.
[4] V. S. Vladimirov, “Equation of Mathematical Physics,” Mir Publication, Moscow, 1984.
[5] G. E. Shilov, “Mathematical Analysis. The Second Special Course,” Nauka, Moscow, 1965.
[6] 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.
[7] 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.
[8] 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

  
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