**Figure 1.**
(**a**) Shows fractional order Chebyshev polynomials with different values of $n$, $\alpha =0.8$. (**b**) Shows fractional order Chebyshev polynomials with n = 4 and different values of $\alpha =0.4,\text{}0.8,\text{}1.2,\text{}1.6$. (**c**) Normalized Chebyshev polynomials with different orders $n=0,\text{}1,\text{}2,\text{}3,\text{}4,\text{}5$. (**d**) Normalized Chebyshev polynomials with $n=4,\text{}\alpha =0.4,\text{}0.8,\text{}1.5$.

**Figure 1.**
(**a**) Shows fractional order Chebyshev polynomials with different values of $n$, $\alpha =0.8$. (**b**) Shows fractional order Chebyshev polynomials with n = 4 and different values of $\alpha =0.4,\text{}0.8,\text{}1.2,\text{}1.6$. (**c**) Normalized Chebyshev polynomials with different orders $n=0,\text{}1,\text{}2,\text{}3,\text{}4,\text{}5$. (**d**) Normalized Chebyshev polynomials with $n=4,\text{}\alpha =0.4,\text{}0.8,\text{}1.5$.

**Figure 2.**
(**a**) Shows GFCPs different value of $n=0,\text{}1,\text{}2,\text{}3,\text{}4,\text{}5$ and $\alpha =0.8,\text{}\eta =1.5$. (**b**) Shows GFCPs different values of $\alpha =0.25,\text{}0.5,\text{}0.75,\text{}1,\text{}1.25,\text{}1.5$ and n = 5. (**c**) Normalized GFCPs different value of $n=0,\text{}1,\text{}2,3,\text{}4,\text{}5$ and $\alpha =1,\text{}\eta =1$. (**d**) Shows normalized GFCPs different values of $\alpha =0.25,\text{}0.5,\text{}0.75,\text{}1,\text{}1.25,\text{}1.5$.

**Figure 2.**
(**a**) Shows GFCPs different value of $n=0,\text{}1,\text{}2,\text{}3,\text{}4,\text{}5$ and $\alpha =0.8,\text{}\eta =1.5$. (**b**) Shows GFCPs different values of $\alpha =0.25,\text{}0.5,\text{}0.75,\text{}1,\text{}1.25,\text{}1.5$ and n = 5. (**c**) Normalized GFCPs different value of $n=0,\text{}1,\text{}2,3,\text{}4,\text{}5$ and $\alpha =1,\text{}\eta =1$. (**d**) Shows normalized GFCPs different values of $\alpha =0.25,\text{}0.5,\text{}0.75,\text{}1,\text{}1.25,\text{}1.5$.

**Figure 3.**
Shows different values GFCPs with different values of $\eta =0.9,1.5,1.9,2.4$.

**Figure 3.**
Shows different values GFCPs with different values of $\eta =0.9,1.5,1.9,2.4$.

**Figure 4.**
(**a**) Shows GFLPs with different orders. (**b**) Shows GFLPs with different value of $\lambda $. (**c**) Shows normalized GFLPs with different orders. (**d**) Shows normalized GFLPs with different values of $\lambda $.

**Figure 4.**
(**a**) Shows GFLPs with different orders. (**b**) Shows GFLPs with different value of $\lambda $. (**c**) Shows normalized GFLPs with different orders. (**d**) Shows normalized GFLPs with different values of $\lambda $.

**Figure 5.**
Original dataset.

**Figure 5.**
Original dataset.

**Figure 6.**
Columns 1 to 4 shows the reconstructed gray-level images with order 16, 50, 100, and 150, respectively, from GFCMs.

**Figure 6.**
Columns 1 to 4 shows the reconstructed gray-level images with order 16, 50, 100, and 150, respectively, from GFCMs.

**Figure 7.**
Comparison of reconstruction errors with different choices of parameters of GFCMs.

**Figure 7.**
Comparison of reconstruction errors with different choices of parameters of GFCMs.

**Figure 8.**
Columns 1 to 4 shows the reconstructed by using GFLMs gray-level images with order 50, 100, 150, and 300, respectively.

**Figure 8.**
Columns 1 to 4 shows the reconstructed by using GFLMs gray-level images with order 50, 100, 150, and 300, respectively.

**Figure 9.**
Comparison of reconstruction errors with different choices of parameters of GFLMs.

**Figure 9.**
Comparison of reconstruction errors with different choices of parameters of GFLMs.

**Figure 10.**
Shows the reconstructed Lena image at the same orders from the different proposed GFCMs, FCMs, Generalized Laguerre Moments (GLMs Algorithm 3 and GFLMs).

**Figure 10.**
Shows the reconstructed Lena image at the same orders from the different proposed GFCMs, FCMs, Generalized Laguerre Moments (GLMs Algorithm 3 and GFLMs).

**Figure 11.**
Shows the Mean Square Error MSE for the different proposed GFCMs, GLMs, and GFLMs compared with FCMs of the Lena image reconstruction error.

**Figure 11.**
Shows the Mean Square Error MSE for the different proposed GFCMs, GLMs, and GFLMs compared with FCMs of the Lena image reconstruction error.

**Figure 12.**
This figure displays the nature logarithm of computational time of moments obtained from different proposed GFCMs, GLMs, GFLMs, and FCM algorithms.

**Figure 12.**
This figure displays the nature logarithm of computational time of moments obtained from different proposed GFCMs, GLMs, GFLMs, and FCM algorithms.