A Novel Conformable Triple Elzaki Transform Decomposition Method for Nonlinear Fractional Telegraph Equations
Keywords:
Conformable Fractional Derivative; Conformable Triple Elzaki Transform; Nonlinear Fractional Telegraph Equation; Adomian’s Polynomial; Conformable Triple Elzaki Decomposition Method.Abstract
This paper introduces a novel hybrid analytical approach, namely the Conformable Triple Elzaki Decomposition Method (CTEDM), for obtaining exact solutions of two-dimensional nonlinear conformable fractional telegraph equations. The proposed method combines the Conformable Triple Elzaki Transform (CTET) with Adomian’s decomposition method to effectively handle both linear and nonlinear components of the problem. Several fundamental properties and theorems of the CTET are established to support the analytical framework. The linear part of the governing equation is solved using the CTET, while the nonlinear terms are efficiently treated via Adomian polynomials. Remarkably, the proposed method requires only a minimal number of iterations to obtain exact or near-exact solutions. To demonstrate the accuracy and applicability of the method, benchmark problems from mathematical physics are considered, and the obtained results show excellent agreement with expected analytical behavior. Compared to existing techniques such as Laplace transform, Reduced Differential Transform Method (RDTM), and classical Adomian decomposition approaches, the proposed CTEDM offers faster convergence, reduced computational complexity, and improved analytical tractability. The results confirm that the method is efficient, reliable, and capable of producing highly accurate solutions with minimal computational effort. Furthermore, the proposed approach has strong potential for extension to a wide class of nonlinear fractional partial differential equations arising in applied mathematics and physics.
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