Kesirli ve klasik lineer olmayan kismi diferansiyel denklemler: Teori ve uygulamalar

This thesis offers some classical and fractional partial differential equations (PDEs) with an extensive study of theory and applications. In order to investigate the integer and non-integer order differential equations (FDEs), several non-local fractional derivatives and local derivatives are applied. Riemann-Liouville (RL), Caputo and Atangana-Baleanu are non-local fractional derivatives whereas local derivatives are conformable (CD), and beta (BD) derivatives. In addition, symmetries and conservation regulations (Cls) play a significant role in determining the inner characteristics, integrability, presence, and uniqueness of differential equation systems. Because of this, the symmetries are investigated for both the classical and fractional differential equations; Cls through the concept of nonlinear self-adjoint (NSA) are also obtained. Moreover, from the perspective of analytical and numerical aspects, the thesis investigates the governing differential equations thus extracting several SW solutions and soliton solutions. To give an invigoration to the analytical and numerical alternatives acquired, numerical simulations are performed.