Nosiba Osman Yuosif Abdalla2022-08-222022-08-222022-05http://hdl.handle.net/123456789/17256Thesis Presented as a Partial Fulfillment for M.Sc IN MATHEMATICSAbstract The ψ-Caputo formula is a generalization of Caputo formula and many definitions by choosing a special kernel. The main aim of this research is to solve nonlinear partial differential equations of the fractional order using ψ-Caputo derivative with some applications. Firstly, the Caputo and ψ-Caputo derivatives was stud- ied. Secondly, nonlinear partial differential equations of the fractional order was solved by using the Variational Iteration Method and the Adomian Decomposi- tion Method. Finally, some a mathematical models using a fractional differential equations was solved.differentialequationsThesis