Thesis

In this thesis, we introduce a modified approach for solving fractional order boundary value problems. This approach is given by applying the Riesz-Feller operator to obtain a modified finite difference equation, which is symmetric to the equation of fractional boundary value problems. Also, the main objective of this work is to study the existence and uniqueness theorem of solutions of the fractional boundary value problems, and to present their proof depending on Schauder fixed point theorem for fractional order integral operator.

In this work the solutions of ordinary homogenous fractional order (with values between zero and one) differential equations with variable coefficients are investigated. Also the existence of the solution is by presenting theorems, using the method of Power Series for ordinary and singular type of fractional order differential equations with variable coefficients. Example has been presented for each case.

The objective of this thesis is to study first the theory of fractional calculus and some of well known methods for evaluating derivatives of fractional orders for certain functions. The second objective is to study the G-spline interpolation functions and its construction using a new approach in formulating the Heremite-Birkhoff problem using fractional derivatives instead of integer order derivatives.