A new formula for fractional integrals of Chebyshev polynomials: application for solving multi-term fractional differential equations (Q358068)

The authors construct an approximate method to solve the differential problem of the form NEWLINE\[NEWLINE D^{\nu}u(x) + \sum^{r-1}_{i=1}\gamma_{i}D^{\beta_{i}}u(x)+ \gamma_{r}u(x)=g(x) \qquad \text{in }(0,L),NEWLINE\]NEWLINE NEWLINE\[NEWLINE u^{(i)}(x)=d_{i}, \quad i=0,1,\dots,m-1,\quad 0<\beta_{i}<\nu,\quad m-1<\nu\leq m,NEWLINE\]NEWLINE where the derivatives \( D^{\nu}\) and \( D^{\beta_{i}}\) 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.NEWLINENEWLINEReviewer's remark: The numerical examples given in this article are not sufficient to prove the convergence of the method.