An extension of picard-lindelöff theorem to fractional differential equations^*

^*This paper was presented in Second International Workshop “Transform Methods & Special Functions”, Varna'96.

Abstract

The method of contraction mapping defined on a complete metric space is used to prove the existence and uniqueness of solutions of the system of differential equations:

together with the initial condition y(x_o)=y_o, where y^(α is the Riemann-Liouville derivative of non integer order a of a real valued vector function y(x), under usual continuity and Lipschitz conditions on the function f. The classical Picard-Lindeloff theorem for ordinary differential equations of integer order is a special case of the main result when α = 1. Some examples are given. Finally, consequences for the linear case are obtained.

Keywords:

• Fractional calculus
• fractional differential equations
• special functions
• Riemann-Liouville
• fractional orde
• non integer order
• generalized order

^*This paper was presented in Second International Workshop “Transform Methods & Special Functions”, Varna'96.

^†Paper partidy supported by DGICYT and by DGUI of G.A.CC.

^*This paper was presented in Second International Workshop “Transform Methods & Special Functions”, Varna'96.

^†Paper partidy supported by DGICYT and by DGUI of G.A.CC.

Notes

^*This paper was presented in Second International Workshop “Transform Methods & Special Functions”, Varna'96.

^†Paper partidy supported by DGICYT and by DGUI of G.A.CC.

Additional information

Notes on contributors

N. Hayek

1

J. Trujillo

1

M. Rivero

2

B. Bonilla

3