Skip to main content

Advertisement

Table 7 Some numerical results of \(\tau (\alpha , b)<1\) in equation (29) in Example 1 for \(q=\frac{1}{7}, \frac{1}{2}, \frac{8}{9}\). Note that \((a)=\varGamma _{q}(\beta _{2}+1)\), \((b)= \varGamma _{q}(2-\beta _{1})\), and \((c) = M(\alpha , b)\)

From: On the existence of solutions for a multi-singular pointwise defined fractional q-integro-differential equation

n\(q =\frac{1}{7}\)\(q =\frac{1}{2}\)\(q =\frac{8}{9}\)
(a)(b)(c)τ(a)(b)(c)τ(a)(b)(c)τ
10.96610.96564.85440.17420.99650.97722.83020.10051.69361.3890.54740.016
20.96440.96424.86850.17490.95650.94933.09150.11171.49231.27330.75660.0231
30.96410.9644.87050.1750.93820.93643.22480.11751.36281.19670.96020.0302
40.96410.9644.87080.1750.92940.93023.2920.12051.27211.14191.15410.0373
50.96410.9644.87090.1750.92510.92723.32580.1221.2051.10071.3360.044
100.96410.9644.87090.1750.9210.92433.35860.12341.0310.99052.05110.072
110.96410.9644.87090.1750.92090.92423.35910.12351.01240.97832.1580.0763
120.96410.9644.87090.1750.92090.92423.35940.12350.99670.96812.25440.0802
130.96410.9644.87090.1750.92090.92423.35950.12350.98330.95932.34130.0838
140.96410.9644.87090.1750.92090.92423.35960.12350.97190.95172.41940.087
150.96410.9644.87090.1750.92090.92423.35960.12350.9620.94522.48960.09
620.96410.9644.87090.1750.92090.92423.35970.12350.89290.89893.0720.1146
630.96410.9644.87090.1750.92090.92423.35970.12350.89290.89893.07230.1147
640.96410.9644.87090.1750.92090.92423.35970.12350.89280.89893.07250.1147