Thesis
Solutions of fractional order delay differential equations. +CD
The Fractional Order Bounded Delay Differential Equations (FOBDDE's) has been studied in this work. The Existence and Uniqueness theorems of such type of differential equation have been proved, by using the successive approximation techniques. Also, the analytic solution of (FOBDDE's) are presented, using Laplace Transformation, and the numerical solutions are discussed, using general one-step methods and linear multi-step methods. The comparison, among these methods and the exact solutions are presented .
Some finite difference methods for solving fractional differential equations. +CD
Laplace transform method for solving ordinary fractional order differential equations with constant coefficients. +CD
Fractional Calculus is a branch of mathematical analysis that satisfies
Modified numerical methods for solving the multi - dimentional integral equations. +CD
Generating normal varieties by Monte Carlo methods for estimating the cumulative distribution function and parameters. +CD
Numerical solution of fuzzy boundary value problems. +CD
This work has three objectives: The first objective is to study fuzzy set theory including definitions, notations and examples. The second objective is to study and proof the existence and uniqueness theorem of fuzzy boundary value problems directly without transforming the problem into fuzzy initial value problem. The third objective is to study the numerical solution of fuzzy boundary value problems.
Solution cauchy type problem of partial fractional order differential equations. +CD
Solution cauchy type problem of partial fractional order differential equations. +CD
In this work, we obtain an analytical solution for Cauchy type problem of partial fractional order differential equation in terms of Mittage - Leffler function using Laplace transformation. The existence and uniqueness of the analytical solution also, is reviewed by reducing the Cauchy type problem of partial fractional order differential equation into linear Volterra integral equation of the second kind and showing that the solution of our Cauchy type problem is equivalent to the solution of linear Volterra integral equation of the second kind.