On Fractional Order Hybrid Differential Equations

We develop the theory of fractional hybrid differential equations with linear and nonlinear perturbations involving the Caputo fractional derivative of order . Using some fixed point theorems we prove the existence of mild solutions for two types of hybrid equations. Examples are given to illustrate the obtained results.

[1]  B. C. Dhage.  A Fixed Point Theorem in Banach Algebras Involving Three Operators with Applications , 2004 .

[2]  Bapurao C. Dhage,et al.  On a fixed point theorem in Banach algebras with applications , 2005, Appl. Math. Lett..

[3]  Hongling Lu,et al.  Theory of fractional hybrid differential equations with linear perturbations of second type , 2013 .

[4]  V. Lakshmikantham,et al.  Basic results on hybrid differential equations , 2010 .

[5]  Carlo Cattani,et al.  Fractional Calculus and Shannon Wavelet , 2012 .

[6]  K. Diethelm,et al.  Fractional Calculus: Models and Numerical Methods , 2012 .

[7]  B. Dhage,et al.  Nonlinear Functional Boundary Value Problems in Banach Algebras Involving Caratheodories , 2006 .

[8]  I. Podlubny.  Fractional differential equations , 1998 .

[9]  R. Hilfer.  Applications Of Fractional Calculus In Physics , 2000 .

[10]  D. Baleanu,et al.  ON THE FRACTIONAL-ORDER DIFFUSION-WAVE PROCESS , 2010 .

[11]  Qiuping Li,et al.  Theory of fractional hybrid differential equations , 2011, Comput. Math. Appl..

[12]  Dumitru Baleanu,et al.  Existence of a periodic mild solution for a nonlinear fractional differential equation , 2012, Comput. Math. Appl..

[13]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies) , 2006 .

[14]  B. Dhage,et al.  Basic results in the theory of hybrid differential equations with linear perturbations os second type , 2012 .

[15]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[16]  Delfim F. M. Torres,et al.  Existence and uniqueness of solutions to functional integro-differential fractional equations , 2012 .

[17]  Zhaosheng Feng,et al.  Positive solutions of fractional differential equations with derivative terms , 2012 .

[18]  Mohamed A. E. Herzallah.  Mild and strong solutions to few types of fractional order nonlinear equations with periodic boundary conditions , 2012 .