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A new formula for fractional integrals of Chebyshev polynomials: application for solving multi-term fractional differential equations. (English) Zbl 1278.65096

The authors construct an approximate method to solve the differential problem of the form

D ν u(x)+ i=1 r-1 γ i D β i u(x)+γ r u(x)=g(x)in(0,L),
u (i) (x)=d i ,i=0,1,,m-1,0<β i <ν,m-1<νm,

where the derivatives D ν and D β i denote the Riemann-Liouville fractional derivatives. The approximate method is constructed using the expansion of the solution by a system of Chebyshev orthogonal polynomials and the notion of integration of fractional order.

Reviewer’s remark: The numerical examples given in this article are not sufficient to prove the convergence of the method.

MSC:
65L05Initial value problems for ODE (numerical methods)
65L03Functional-differential equations (numerical methods)
34A08Fractional differential equations
34A30Linear ODE and systems, general