Mathematics and Computer Applications - Sciene

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.

      In this work, Linear Programming Problems have been implemented to build four linear models for projects management. An Interior – Point Method has been implemented to solve such linear models, instead of using the usual techniques "Simplex Method", by implementing the "what's Best 9.0 " software, and obtaining the critical path in minimum completion time, minimum crashing cost and optimal total ( direct & indirect ) costs for a simple real project.

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.