Theses and Dissertations

Date of Award


Document Type


Degree Name

Master of Science (MS)



First Advisor

Mohammad Bhatti

Second Advisor

Soma Mukherjee

Third Advisor

Nikolaos Dimakis


This thesis uses B-Polynomial bases to solve both one-dimensional and multi-dimensional linear and nonlinear partial differential equations and linear and nonlinear fractional differential equations. The approach involves constructing an operational matrix from the terms of these equations using Caputo's fractional derivative of fractional B-polynomials. This leads to a semi-analytical solution derived from a matrix equation, and the results obtained using this method are compared to analytical and numerical solutions presented by other authors. The method is shown to be effective in calculating approximate solutions for various differential equations and provides a higher accuracy level than finite difference methods. This technique can also be extended to solve more complex linear, nonlinear, partial, and fractional differential equations in multivariable problems.


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