Applications of the Novel (𝐺^′/𝐺)-Expansion Method for a Time Fractional Simplified Modified Camassa-Holm (MCH) Equation

Table 1

Comparison between our solutions and Liu et al. [48] solutions.

Obtained solutions	Liu et al. [48] solutions
(i) If 𝐿=1,𝐴=2,𝐵=0,𝐶=2,𝛿=−1,𝛾=1,𝑘=0,𝛼=1,; and 𝑢^11(𝜉)=𝑢1,2(𝑥,𝑡), then the solution is; 𝑢1,2()2𝑥,𝑡=±2tanh𝑥+3𝑡.	(i) If 𝐶1=1,𝐶2=0,𝜆=2,𝜇=0,𝑎=1,and𝑘=1,; then the solution is; 𝑢1,2()2𝑥,𝑡=±2tanh𝑥+3𝑡.
(ii) If 𝐿=1,𝐴=2,𝐵=1,𝐶=3,𝛿=−1,𝛾=1,𝑘=0,𝛼=1,; and 𝑢1^12(𝜉)=𝑢3,4(𝑥,𝑡), then the solution is; 𝑢3,4(𝑥,𝑡)=±2√3tan(𝑥+2𝑡).	(ii) If 𝐶1=1,𝐶2=0, 𝜆^2−4𝜇=−4, 𝑎=1,and𝑘=1,; then the solution is; 𝑢3,4(𝑥,𝑡)=±2√3tan(𝑥+2𝑡).
(iii) If 𝐿=1,𝐴=0,𝐵=0,𝐶=2,𝛿=−1,𝛾=1,𝑘=0,; 𝛼=1,𝑐2=0, and 𝑢1^25(𝜉)=𝑢3,4(𝑥,𝑡), then the solution is; 𝑢3,4(𝑥,𝑡)=±2√31𝑥+2𝑡.	(iii) If 𝐶1=1,𝐶2=1,𝜆=2,𝜇=1,𝑎=1,and𝑘=−1,; then the solution is; 𝑢3,4(𝑥,𝑡)=±2√31𝑥+2𝑡.
(iv) If 𝐿=1,𝐴=2,𝐵=0,𝐶=2,𝛿=1,𝛾=1,𝑘=0,𝛼=1,; and 𝑢^11(𝜉)=𝑢1,2(𝑥,𝑡), then the solution is; 𝑢3,4()2𝑥,𝑡=±2𝑖tanh𝑥−3𝑡.	(iv) If 𝐶1=1,𝐶2=0,𝜆=2,𝜇=0,𝑎=1,and𝑘=1,; then the solution is; 𝑢3,4()2𝑥,𝑡=±2𝑖tanh𝑥−3𝑡.
(v) If 1𝐿=1,𝐴=1,𝐵=2,𝐶=3,𝛿=−1,𝛾=1,𝑘=0,𝛼=1,; and 𝑢1^12(𝜉)=𝑢3,4(𝑥,𝑡), then the solution is; 𝑢3,4(𝑥,𝑡)=±√16𝑖tan2(𝑥−4𝑡).	(v) If 𝐶1=1,𝐶21=0,𝜆=0,𝜇=4,𝑎=1,and𝑘=1,; then the solution is; 𝑢3,4(𝑥,𝑡)=±√16𝑖tan2(𝑥−4𝑡).
(vi) If 𝐿=1,𝐴=0,𝐵=0,𝐶=2,𝛿=1,𝛾=1,𝑘=0,; 𝛼=1,𝑐2=0, and 𝑢1^25(𝜉)=𝑢3,4(𝑥,𝑡), then the solution is; 𝑢3,4(𝑥,𝑡)=±𝑖2√31𝑥−2𝑡.	(vi) If 𝐶1=1,𝐶2=1,𝜆=2,𝜇=1,𝑎=1,and𝑘=1,; then the solution is; 𝑢3,4(𝑥,𝑡)=±𝑖2√31𝑥−2𝑡.