الفهرس 
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Abstract
The use of fractionalorders differential and integral operators in mathematical models has become increasingly widespread in recent years. Several forms of fractional order differential equations have been proposed in standard models, and there has been significant interest in developing numerical schemes for their solutions. However, much of the work published to date has been concerned with linear single term equations and, of these, equations of order less than unity have been most often investigated. The thesis consists of three chapters: Chapter 1. This chapter collects the main concepts of fractionalorder integration, fractionalorder differentiation, and their properties. Also it contains a survey on the numerical solution of fractional order differential equations. Chapter 2. In this chapter we focus on providing a numerical solution to nonlinear multiterm fractional (arbitrary) orders differential equation by transforming it to a system of first order differential equations. Existence and uniqueness of such solution is discussed. Methods ET, ER, 2E and 3E are suggested. Chapter 3. In this chapter we focus on providing a numerical solution to nonlinear multiterm fractional (arbitrary) orders differential equation by transforming it to a system of nonlinear integral equations. Existence and uniqueness of such solution is proved. We solve the resulting system by the PECE method.