Abstract
In this paper we use a family of Muntz polynomials and a computational technique based on the collocation method to solve the calculus variation problem. This approach is utilizedto reduce the solution of linear and nonlinear fractional order dierential equations to the solution of a system of algebraic equations. Thus we can obtain a good approximation evenby using a smaller of collocation points.
Highlights
Preliminaries and notationWe present a short overview to the fractional calculus [11,10,9]
In this paper we use a kind of the Müntz-Legendre polynomials such that their fractional derivatives be Müntz-Legendre polynomials again
According to the above definitions it is clear that for a = 0, the Caputo fractional derivative is equal to the left hand side Caputo fractional derivative
Summary
We present a short overview to the fractional calculus [11,10,9]. In this sequel, we suppose α ∈ (0, 1) and Γ represents the Gamma function. The fractional derivative of f in the Caputo sense is defined for f ∈ C1[0, 1] as CDxαf (x). The left and right hand sides Caputo fractional derivatives of order α are defined for f ∈ C1[0, 1] as CaDxαf (x). (t − x)−αf ′(t)dt, x x ∈ [0, 1], respectively. According to the definition of right hand side Caputo derivative [10], we get CaDxαxβ. For the simplification the notation D∗α is used instead of CaDxα
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