Numerical schemes for variable exponent fractional‐type integral equations

摘要

In this study, two predictor–corrector schemes are developed for the numerical solution of variable exponent fractional‐type integral equations. The proposed schemes considered a Volterra‐type integral equation and then employed Trapezoidal and Simpson's 1/3 rules to obtain numerically approximate solutions. Some test problems are examined to demonstrate the performance, validity, and effectiveness of the proposed schemes. Comparisons are made between the proposed schemes to highlight the accuracy and convergence of these techniques. As an application, the effect of the variable‐order exponent on the dynamics of the studied systems is discussed.