An Arbitrary (Fractional) Orders Differential Equation with Internal Nonlocal and Integral Conditions
Ahmed El-Sayed, E. Bin-Taher
DOI: 10.4236/apm.2011.13013   PDF    HTML     5,702 Downloads   11,839 Views   Citations

Abstract

In this paper we study the existence of solution for the differential equation of arbitrary ( fractional) orders,with the general form of internal nonlocal condition,The problem with nonlocal integral condition will be studied.

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A. El-Sayed and E. Bin-Taher, "An Arbitrary (Fractional) Orders Differential Equation with Internal Nonlocal and Integral Conditions," Advances in Pure Mathematics, Vol. 1 No. 3, 2011, pp. 59-62. doi: 10.4236/apm.2011.13013.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] A. Boucherif, “First-Order Differential Inclusions with Nonlo-cal Initial Conditions,” Applied Mathematics Letters, Vol. 15, No. 4, 2002, pp. 409-414. doi:10.1016/S0893-9659(01)00151-3
[2] A. Boucherif, “Nonlocal Cauchy Problems for First-Order Multivalued Dif-ferential Equations,” Electronic Journal of Differential Equa-tions, Vol. 47, 2002, pp. 1-9.
[3] A. Boucherif and R. Precup, “On the Nonlocal Initial Value Problem for First Order Differ-ential Equations,” Fixed Point Theory, Vol. 4, No. 2, 2003, pp. 205-212.
[4] A. Boucherif, “Semilinear Evolution Inclusions with Nonlocal Conditions,” Applied Mathematics Letters, Vol. 22, No. 8, 2009, pp. 1145-1149. doi:10.1016/j.aml.2008.10.004
[5] M. Benchohra, E. P. Gat-sori and S. K. Ntouyas, “Existence Results for Seme-Linear Integrodifferential Inclusions with Nonlocal Conditions,” Rocky Mountain Journal of Mathematics, Vol. 34, No. 3, 2004。
[6] M. Benchohra, S. Hamani and S. K. Ntouyas, “Boundary Value Problems for Differential Equations with Fractional Order and Nonlocal Conditions,” Nonlinear Analysis: Theory, Methods & Applications, Vol. 71, No. 7-8, 2009, pp. 2391-2396. doi:10.1016/j.na.2009.01.073
[7] R. F. Curtain and A. J. Pritchard, “Functional Analysis in Modern Applied Mathematics,” Academic Press, London, 1977.
[8] K. Deim-ling, “Nonlinear Functional Analysis,” Springer- Verlag, Berlin, 1985.
[9] J. Dugundji and A. Granas, “Fixed Point Theory,” Monografie Mathematyczne, Polska Akademia Nauk, War-szawa, Vol. 1, 1982.
[10] A. M. A. El-Sayed and Sh. A. Abd El-Salam, “On the Stability of a Fractional Order Differential Equation with Nonlocal Initial Condition,” Electronic Journal of Qualitative Theory of Differential Equations, Vol. 2009, No. 29, 2008, pp. 1-8.
[11] A. M. A. El-Sayed and E. O. Bin-Taher, “A Nonlocal Problem of an Arbitrary (Fractional) Orders Dif-ferential Equation,” Alexandria Journal of Mathematics, Vol. 1, No. 2, 2010, pp. 1-7.
[12] E. Gatsori, S. K. Ntouyas and Y. G. Sficas, “On a Nonlocal Cauchy Problem for Differential Inclu-sions,” Abstract and Applied Analysis, Vol. 2004, No. 5, 2004, pp. 425-434.
[13] G. M. N’Guérékata, “A Cauchy Problem for Some Fractional Abstract Differential Equation with Non Local Conditions,” Nonlinear Analysis: Theory, Methods & Applica-tions, Vol. 70, No. 5, 2009, pp. 1873-1876. doi:10.1016/j.na.2008.02.087
[14] I. Podlubny, “Fractional Differential Equations,” Academic Press, San Diego, New York and London, 1999.
[15] I. Podlubny and A. M. A. EL-Sayed, “On Two Definitions of Fractional Calculus,” Pre-print UEF 03-96, ISBN 80-7099-252-2, Institute of Experi-mental Physics, Slovak Academy of Science, 1996.

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