A numerical technique for solving various kinds of fractional partial differential equations via Genocchi hybrid functions

Abstract

In the current study, a new technique for solving various kinds of fractional partial differential equations based upon Genocchi hybrid functions (GHFs) is projected. Genocchi hybrid collocation technique by utilizing delay operational matrix, integer and the fractional operational matrix of the derivative is introduced. We calculate the delay operational matrix without error, this matrix is a reason to achieve the approximate solution with high accuracy. These operational matrices are applied to convert the proposed equations to a set of algebraic equations with unknown GHFs coefficients. Also, we investigate the error analysis based on Sobolev space. At last, several examples are examined with graphs and tables to demonstrates the efficiency and accuracy of the numerical plan.