Chebyshev Polynomials of Sixth Kind for Solving Nonlinear Fractional PDEs with Proportional Delay and Its Convergence Analysis

Algorithm 1

Solution method

Input:

Step 1. Derive operational matrices , , and from (21), (29), and (36).

Step 2. Construct the operational matrices , , , , , from (46)-(49).

Step 3. Consider the approximation in (51).

Step 4. Find approximations to , , , and from (52)-(55).

Step 5. Find an approximation to from (57).

Step 6. Determine the residual function from (61).

Step 7. Obtain roots of and () using command in Maple.

Step 8. Collocate the residual function at tensor points .

Step 9. Solve the resultant non-linear system in Step 8 by Newton’s iteration method and obtain the unknown vector .

Step 10. Find from (54).

Output: