The College of Science, Department of Mathematics, discussed a Ph.D. thesis entitled "Spline Techniques for Solving Some Fractional-Time Partial Differential Equations" by postgraduate student Fahd Kamel Nashmi. The dissertation aims to study fractional partial differential equations (FPDEs) as an extended formulation of classical partial differential equations (PDEs) and to use the four-spline method to find the numerical solution of fractional-time partial differential equations and fractional-time telegraph equations. The dissertation included the use of different types of B-splines to calculate the numerical solutions of linear and nonlinear fractional-time partial differential equations. She explained that the main reason for using B-splines to solve partial differential equations numerically is their local support property, which provides support for B-spline functions in certain intervals (i.e., they are zero otherwise and non-zero in specific intervals), and the use of finite difference techniques decomposes the time derivatives, and B-spline functions perform spatial approximation.
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