Abstract
Nowadays, the operational matrix plays an important role in
solving problems with partial, ordinary or fractional derivatives. In the
current study, we construct the operational matrix of the fractional integral
for cubic B-spline scaling function and wavelets and it applies to solve varieties of the fractional integro-differential equations. To do this, firstly,
the operational matrix of fractional integral for Haar scaling functions is
constructed by using the definition of the Riemann-Liouville fractional
integral operator and the orthogonal projection of polynomial on space of
Haar scaling functions. Afterward, we obtain the operational matrix of
cubic B-spline functions from fractional order using approximation cubic
B-spline functions with Haar scaling functions and collocation method.
The principal characteristics of this method are as follows: The operational matrix of cubic B-spline functions is obtained simply because of the
useful properties of the Haar scaling functions, reducing the time, the less
occupation of the computer memory which converts to a system of linear
and nonlinear equations. Finally, we will show the validity and efficiency
of the new method by numerical examples and convergence analysis.
Hamid Mesgarani, Hamid Safdariı, Abolfazl Ghasemian, Yones Esmaeelzade. (2019) The Cubic B-spline Operational Matrix Based on Haar Scaling Functions for Solving Varieties of the Fractional Integro-differential Equations, Punjab University Journal of Mathematics, Volume 51, Issue 8.
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