Genocchi polynomials for variable-order time fractional Fornberg–Whitham type equations

Abstract

In this research, a kind of non-singular variable-order fractional derivative is utilized to define two types of variable-order fractional Fornberg–Whitham equations. The shifted Genocchi polynomials are employed to construct two operational matrix approaches for solving these equations. More precisely, a new variable-order fractional derivative matrix is obtained for these polynomials, and used with the collocation technique for solving these equations. In fact, using this approaches, solving such problems converts into solving simple systems of algebraic equations. Some examples are solved to illustrate the applicability and accuracy of the proposed algorithms.

Keywords

• Variable-order fractional derivative
• Genocchi polynomials
• Fornberg–Whitham equation
• Fractional derivative matrix