ELZAKI TRANSFORM METHOD FOR FRACTIONAL ORDER LINEAR AND NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

Abstract

This thesis utilizes a novel methodology based on the Elzaki transform method (ETM) combined with the Homotopy perturbation technique to derive solutions for a collection of time-fractional partial differential equations (TFPDEs), employing the Caputo definition of fractional derivatives. Building on similar previous works, this analysis explores real-world applications of these theoretical concepts. MAPLE software is used to produce visual representations of the solutions. Furthermore, a thorough examination of absolute errors is conducted, with the results presented in an organized tabular format. The findings indicate that the proposed method is both efficient and effective for obtaining approximate solutions to time-fractional partial differential equations. In particular, this approach facilitates the accurate computation of solutions that align closely with empirical data across a range of time-fractional differential contexts. Future research may explore the potential of this technique to tackle broader categories of fractional calculus challenges. In summary, the innovative Elzaki-Homotopy method shows significant potential for solving time-fractional partial differential equations (TFPDEs) that arise in the fields of advanced mathematical physics and engineering.