Change point detection tries to identify times when the probability distribution of a stochastic process or time series changes. In this paper, we replace the traditional penalty terms for both ridge and lasso parts in elastic net with corresponding fusion format. Fusion penalty encourages sparsity in the differences between successive coefficients, combine with the use of first and second order fusion penalty we would be able to transform it to elastic net fashion by using a transformation matrix. Adding the second order fusion penalty instead of lasso penalty in fused lasso help us avoid the estimations equals to 0. Also, we use the coordinate descent algorithm to estimate the coefficients and compare different parameter features. Finally, we check the performance of change point detection in detecting mean changes and relate the parameter lambda with the number of changes detected and the change point score in different scenarios.