Application of Fractional Order Legendre Polynomials: a New Procedure for Solution of Linear and Nonlinear Fractional Differential Equations under $m$-point Nonlocal Boundary Conditions
| Autor: | Rahmat Ali Khan, Hammad Khalil, Mohammed Mehdi Rashidi |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Fractional differential equations
lcsh:T57-57.97 Mathematical analysis Order (ring theory) 010103 numerical & computational mathematics General Medicine Mixed boundary condition 01 natural sciences 010101 applied mathematics Nonlinear system Algebraic equation Fractional order Legendre polynomials $m$-point boundary value problems Scheme (mathematics) ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION lcsh:Applied mathematics. Quantitative methods Free boundary problem Boundary value problem 0101 mathematics Legendre polynomials Mathematics |
| Zdroj: | Communications in Numerical Analysis, Vol 2016, Iss 2, Pp 144-166 (2016) |
| ISSN: | 2193-4215 |
| Popis: | In this paper, we have proposed a new formulation for the solution of a general class of fractional differential equations (linear and nonlinear) under $\hat{m}$-point boundary conditions. We derive some new operational matrices and based on these operational matrices we develop scheme to approximate solution of the problem. The scheme convert the boundary value problem to a system of easily solvable algebraic equations. We show the applicability of the scheme by solving some test problems. The scheme is computer oriented. |
| Databáze: | OpenAIRE |
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