Homotopy Analysis Method for Solving Fuzzy Variable – Order Fractional Partial Differential Equations with Proportional Delay

Abstract

This paper focuses on providing a semi-analytic approach for the approximate solutions of fuzzy variable-order fractional partial differential equations with Proportional delay, the fractional order derivative will be in the Caputo sense. The solutions according to this approach are easily computed as a convergent power series. The effectiveness of the proposed method is demonstrated through some illustrative examples.

Keywords

• delay partial differential equations
• homotopy analysis method
• fuzzy set theory
• fractional calculus