Bivariate Chebyshev polynomials of the fifth kind for variable-order time-fractional partial integro-differential equations with weakly singular kernel

Abstract The shifted Chebyshev polynomials of the fifth kind (SCPFK) and collocation method are employed to achieve approximate solutions a category functional equations, namely variable-order time-fractional weakly singular partial integro-differential equations (VTFWSPIDEs). A pseudo-operational matrix (POM) approach is developed for numerical solution problem under study. suggested changes solving VTFWSPIDE into system linear algebraic equations. Error bounds obtained, application proposed scheme examined on five problems. results confirm applicability high accuracy fractional