On Fractional Differential Equations

In this thesis, we collect some results on sufficient conditions for the existence and unique of solutions for various classes of initial and boundary value problem for fractional differential equations involving the Caputo fractional derivative. Although the tools of fractional calculus have been available and applicable to various fields of study, the investigation of the theory of fractional differential equations has only been started quite recently. The differential equations involving Caputo differential operators of fractional order, appear to be important in modeling several physical phenomena and therefore seem to deserve an independent study of their theory parallel to the well-known theory of ordinary differential equations. In this thesis, we shall study systematically the basic theory of fractional differential equations involving Caputo differential operators. We follow the method of deducing the basic existence and uniqueness results from the fixed point theory. Keywords: Boundary Value Problems, Fractional Differential Equation, Fractional Calculus