The operational matrix of Caputo fractional derivatives of modified generalized Laguerre polynomials and its applications

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 2 $c_{0}$ , $c_{1}$ , $c_{2}$ and $c_{3}$ for different values of α and β for Example 2

α	β	$c_{0}$	$c_{1}$	$c_{2}$	$c_{3}$	α	β	$c_{0}$	$c_{1}$	$c_{2}$	$c_{3}$
0	1	6	−18	18	−6	0	2	$\frac{3}{4}$	$- \frac{9}{4}$	$\frac{9}{4}$	$- \frac{3}{4}$
1		24	−36	24	−6	1		3	$- \frac{9}{2}$	3	$- \frac{3}{4}$
2		60	−60	30	−6	2		$\frac{15}{2}$	$- \frac{15}{2}$	$\frac{15}{4}$	$- \frac{3}{4}$
3		120	−90	36	−6	3		15	$- \frac{45}{4}$	$\frac{9}{2}$	$- \frac{3}{4}$
4		210	−126	42	−6	4		$\frac{105}{4}$	$- \frac{63}{4}$	$\frac{21}{4}$	$- \frac{3}{4}$
0	3	$\frac{2}{9}$	$\frac{2}{3}$	$\frac{2}{3}$	$- \frac{2}{9}$	0	4	$\frac{3}{32}$	$- \frac{9}{32}$	$\frac{9}{32}$	$- \frac{3}{32}$
1		$\frac{8}{9}$	$- \frac{4}{3}$	$\frac{8}{9}$	$- \frac{2}{9}$	1		$\frac{3}{8}$	$- \frac{9}{16}$	$\frac{3}{8}$	$- \frac{3}{32}$
2		$\frac{20}{9}$	$- \frac{20}{9}$	$\frac{10}{9}$	$- \frac{2}{9}$	2		$\frac{15}{16}$	$- \frac{15}{16}$	$\frac{15}{32}$	$- \frac{3}{32}$
3		$\frac{40}{9}$	$- \frac{30}{9}$	$\frac{4}{3}$	$- \frac{2}{9}$	3		$\frac{15}{8}$	$- \frac{45}{32}$	$\frac{9}{16}$	$- \frac{3}{32}$
4		$\frac{70}{9}$	$- \frac{14}{3}$	$\frac{14}{9}$	$- \frac{2}{9}$	4		$\frac{105}{32}$	$- \frac{63}{32}$	$\frac{21}{32}$	$- \frac{3}{32}$