Some mathematical modeling of fractional order differential equations

This thesis consists of six chapters. In the first chapter, basic concepts and fractional order differential equations are given. In the second chapter, new exact solutions of the modified bad and good Boussinesq equations with Conformable fractional derivatives are obtained using the exponential function method. In the third chapter, a new fractional SIQRV model was developed, numerical applications and stability analysis were performed. In the fourth chapter, the fractional PSQp smoking model and the fractional SAQ alcohol model were created. In addition, numerical applications and stability analysis of the models were performed. In the fifth chapter, the fractional psychological disease model and the fractional dog population model were created by numerical applications and stability analysis were performed. In addition, a new numerical application of the fractional glucose-insulin model was made. Finally, in the sixth chapter, an overall evaluation of the thesis is made.