Solutions of random fractional differential equations using elzaki-adomian and elzaki homotopy analysis method

In this thesis study, in order to obtain the approximate analytical solution of fractional ordinary and partial differential equations and differential equation systems, the initial conditions or coefficients of which are selected from continuous probability distributions and transformed into randomness, the methods that are frequently used in the literature are; Hybrid methods in which the Adomian Decomposition Method and Homotopy Analysis Method are used together with the Elzaki Transformation method are ED-AAM and ED-HAM. The fractional derivatives used here are local and Caputo derivatives. The equations were transformed into random by using smooth, normal, gamma and beta distributions from continuous probability distributions. Expected values, variances and security intervals were calculated from the probability characteristics of the obtained solutions, and the graphs of the found solutions were drawn with the help of MATLAB or MAPLE package programs.