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The construction of operational matrix of fractional derivatives using B-spline functions. (English) Zbl 1276.65015
Summary: Fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. For that reason we need a reliable and efficient technique for the solution of fractional differential equations. Here we construct the operational matrix of a fractional derivative of order \(\alpha \) in the Caputo sense using the linear B-spline functions. The main characteristic behind the approach using this technique is that it reduces such problems to those of solving a system of algebraic equations thus we can solve directly the problem. The method is applied to solve two types of fractional differential equations, linear and nonlinear. Illustrative examples are included to demonstrate the validity and applicability of the new technique presented in the current paper.

MSC:
65D25 Numerical differentiation
65D07 Numerical computation using splines
35R11 Fractional partial differential equations
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
26A33 Fractional derivatives and integrals
34K37 Functional-differential equations with fractional derivatives
34A08 Fractional ordinary differential equations and fractional differential inclusions
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