On a unique solution of fractional differential system
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Abstract
The aim of the study is to investigate the existence and uniqueness of solutions for a semi linear fractional differential system via Banach fixed point theorem. The study proved the existence and uniqueness of solution for a fractional differential system with initial conditions by using contraction mapping theorem, existence and uniqueness results are obtained. Some examples are chosen to illustrate the validity of our results.
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References
[1] Kilbas, A.A.; Trujillo J.J. and Srivastava, H.M. (2006). Theory and Application of Fractional Differential Equations. First edition, Amsterdam: Elsevier: 539.
[2] Miller, K. and Ross, B.(1993). Introduction to the Fractional Calculus and Fractional Differential Equations. First edition. New York: John Wiley and Sons Inc.:376.
[3] Podlubny,I. and Thimann, K.V.(1998). Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. First edition, San Diego: Academic Press:366.
[4] Yu,C. and Gao,G.(2005). Existence of Fractional Differential Equations. Journal of Mathematical Analysis and Applications.,310:26-29
[5] Zhai, C. (2009). Positive Solutions for Third Order Sturm-Liouville Boundary Value Problem with p - Laplacian. Electronic Journal of Differential Equations, 2009 (154):1-9
[6] Delbosco, D. and Rodino, L. (1996). Existence and Uniqueness for a Nonlinear Fractional Differential Equations, Journal of Mathematical Analysis and Applications, 204:609-625.
[7] Benchohra, M. and Hamani, S. (2008). Boundary Value Problem for Differential Equations with Fractional Order, Surveys in Mathematics and Its Application, 3:1-12.
[8] Plotnikov, V.A. and Vityuk. (1999). Differential Equations with a Multivalued Right-Hand Side, Asymptotic Methods. First edition, Odessa: Astroprint: 356.
[9] Girg, P.; Roca, F. and Villegas, S.(2005). Semi Linear Sturm - Liouville Problem with Periodic Nonlinearity. Nonlinear Analysis, 61:1157-1178.
[10] Jaradat, O.K.; Al-Omari, A. and Momani, S.(2008). Existence of the Mild Solution for Fractional Semi Linear Initial Value Problem. Nonlinear Analysis.69 (9):3153-3159.
[11] Mourad, E.; Ismail, H. and Koelink, E.(2005). Theory and Applications of Special Functions. 1st edition, USA: Krishnasami Alladi: Springer:504.
[12] N'guerekata, G.M. (2009). A Cauchy Problem for Some Fractional Abstract Differential Equations with Nonlocal Condition, Nonlinear Analysis. 70 (5):1873-1876.
[13] Granas, A. and Dugundji, J. (2003). Fixed Point Theory. First edition, New York: Springer-Verlag: 707.