Mohammed M. MATAR

NONLOCAL INTEGRO-DIFFERENTIAL EQUATIONS WITH ARBITRARY FRACTIONAL ORDER

In this paper, we investigate the existence and uniqueness of some nonlocal boundary condition for fractional integro-di erential equations with any order. The results are obtained by using xed point theorems. An example is introduced to illustrate the theorem.

Keywords:

Fractional integro-dierential equations; Nonlocal condition; Exis- tence and Uniqueness; Fixed point theorem,

PDF

___

[1] Agrawal, R. P., Benchohra, M., Hamani, S., Boundary value problems for fractional dieren- tial equations, Georgian Mathematical Journal, 16(3)(2009), 401-411.
[2] Agarwal, R. P., Ahmad B., Existence theory for anti-periodic boundary value problems of fractional dierential equations and inclusions, Computers & Mathematics with Applica- tions, 62(2011), 1200-1214.
[3] Balachandran, K., Park, J. Y., Nonlocal Cauchy problem for abstract fractional semilinear evolution equations, Nonlinear Analysis, 71(2009), 4471-4475.
[4] Benchohra, M., Hamani, S., and Ntouyas S. K., Boundary value problems for dierential equations with fractional order and nonlocal conditions, Nonlinear Analysis, 71(2009), 2391- 2396.
[5] N'guerekata, G. M., A Cauchy problem for some fractional abstract dierential equation with nonlocal condition, Nonlinear Analysis, 70(2009), 1873-1876.
[6] Delbosco, D., Rodino, L., Existence and uniqueness for a fractional dierential equation, Journal of Mathematical Analysis and Applications, 204(1996), 609-625.
[7] Matar M. M., Trujillo, J. J.,Existence of local solutions for dierential equations with arbi- trary fractional order, Arabian Journal of Mathematics, DOI 10.1007/s40065-015-0139-4
[8] Jaradat, O. K., Al-Omari, A., and Momani, S., Existence of the mild solution for fractional semilinear initial value problem, Nonlinear Analysis, 69(2008), 3153-3159.
[9] Lakshmikantham, V., Theory of fractional functional dierential equations, Nonlinear Anal- ysis, 69(2008), 3337-3343.
[10] Matar, M., On existence and uniqueness of the mild solution for fractional semilinear integro- dierential equations, Journal of Integral Equations and Applications, 23(3)(2011), 1-10.
[11] Matar, M., Existence and uniqueness of solutions to fractional semilinear mixed Volerra- Fredholm integrodierential equations with nonlocal conditions, Electronic Journal of Dier- ential Equations, 155(2009), 1-7.
[12] Matar, M., Boundary value problem for fractional integro-dierential equations with nonlocal conditions, International Journal of Open Problems in Computer Science and Mathematics, 3(4)(2009), 481-489.
[13] Matar, M., El-Bohisie, F. A., On Existence of Solution for Higher-order Fractional Dieren- tial Inclusions with Anti-periodic Type Boundary conditions, British Journal of Mathematics & Computer Science, 7(5)(2015), 328-340.
[14] Kilbas, A. A., Srivastava, H. M., and Trujillo, J. J., Theory and applications of fractional dierential equations, Elsevier, Amsterdam, 2006.
[15] Podlubny, I., Fractional dierential equations, Academic Press, New York, 1999.
[16] Zaslavsky, G. M., Hamiltonian Chaos and Fractional Dynamics, Oxford University Press, Oxford, UK, 2005.
[17] Magin, R. L., Fractional Calculus in Bioengineering, Begell House Publisher, Connecticut, Conn, USA, 2006.