A method for solving differential equations of fractional order

In this paper, we consider Caputo type fractional differential equations of order 0<@a<1 with initial condition x(0)=x"0. We introduce a technique to find the exact solutions of fractional differential equations by using the solutions of integer order differential equations. Generalization of the technique to finite systems is also given. Finally, we give some examples to illustrate the applications of our results.

[1]  K. Diethelm.  AN ALGORITHM FOR THE NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER , 1997 .

[2]  N. Ford,et al.  The numerical solution of linear multi-term fractional differential equations: systems of equations , 2002 .

[3]  R. Feynman,et al.  RECENT APPLICATIONS OF FRACTIONAL CALCULUS TO SCIENCE AND ENGINEERING , 2003 .

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

[5]  Mariusz Ciesielski,et al.  A Numerical Method for Solution of Ordinary Differential Equations of Fractional Order , 2001, PPAM.

[6]  R. Metzler,et al.  Relaxation in filled polymers: A fractional calculus approach , 1995 .

[7]  T F Nonnenmacher,et al.  A fractional calculus approach to self-similar protein dynamics. , 1995, Biophysical journal.

[8]  K. Diethelm.  The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type , 2010 .

[9]  E. Demirci,et al.  A Fractional Order SEIR Model with Density Dependent Death Rate ABSTRACT | FULL TEXT , 2011 .

[10]  Luise Blank,et al.  Numerical Treatment of Differential Equations of Fractional Order , 1996 .

[11]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[12]  C. F. Lorenzo,et al.  Chaos in a fractional order Chua's system , 1995 .

[13]  N. Ford,et al.  A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations , 2013 .

[14]  E. Ahmed,et al.  Equilibrium points, stability and numerical solutions of fractional-order predator–prey and rabies models , 2007 .

[15]  Igor Podlubny,et al.  Geometric and Physical Interpretation of Fractional Integration and Fractional Differentiation , 2001, math/0110241.

[16]  V. Lakshmikantham,et al.  THEORY OF FRACTIONAL DIFFERENTIAL INEQUALITIES AND APPLICATIONS , 2007 .

[17]  A. Oustaloup.  From fractality to non integer derivation: a fundamental idea for a new process control strategy , 1988 .