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Full-Text Articles in Physical Sciences and Mathematics
Numerical Simulations For Fractional Differential Equations Of Higher Order And A Wright-Type Transformation, Mariana Nacianceno, Tamer Oraby, Hansapani Rodrigo, Y. Sepulveda, Josef A. Sifuentes, Erwin Suazo, T. Stuck, J. Williams
Numerical Simulations For Fractional Differential Equations Of Higher Order And A Wright-Type Transformation, Mariana Nacianceno, Tamer Oraby, Hansapani Rodrigo, Y. Sepulveda, Josef A. Sifuentes, Erwin Suazo, T. Stuck, J. Williams
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
In this work, a new relationship is established between the solutions of higher fractional differential equations and a Wright-type transformation. Solutions could be interpreted as expected values of functions in a random time process. As applications, we solve the fractional beam equation, fractional electric circuits with special functions as external sources, and derive d’Alembert’s formula for the fractional wave equation. Due to this relationship, we present two methods for simulating solutions of fractional differential equations. The two approaches use the interpretation of the Caputo derivative of a function as a Wright-type transformation of the higher derivative of the function. In …
Employing A Fractional Basis Set To Solve Nonlinear Multidimensional Fractional Differential Equations, Md. Habibur Rahman, Muhammad I. Bhatti, Nicholas Dimakis
Employing A Fractional Basis Set To Solve Nonlinear Multidimensional Fractional Differential Equations, Md. Habibur Rahman, Muhammad I. Bhatti, Nicholas Dimakis
Physics and Astronomy Faculty Publications and Presentations
Fractional-order partial differential equations have gained significant attention due to their wide range of applications in various fields. This paper employed a novel technique for solving nonlinear multidimensional fractional differential equations by means of a modified version of the Bernstein polynomials called the Bhatti-fractional polynomials basis set. The method involved approximating the desired solution and treated the resulting equation as a matrix equation. All fractional derivatives are considered in the Caputo sense. The resulting operational matrix was inverted, and the desired solution was obtained. The effectiveness of the method was demonstrated by solving two specific types of nonlinear multidimensional fractional …
A Novel Technique To Solve Fractional Differential Equations Using Fractional-Order B-Polynomial Basis Set, Md Habibur Rahman
A Novel Technique To Solve Fractional Differential Equations Using Fractional-Order B-Polynomial Basis Set, Md Habibur Rahman
Theses and Dissertations
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 …