Analytical Solutions of Fractional Differential Equations via the Variational Iteration Method within the Modified Conformable Fractional Derivative

Abstract

In this paper, we develop a variational iteration method for solving linear and nonlinear fractional differential equations within the modified conformable calculus framework. Rather than reducing the fractional system to integer-order derivatives, we construct the correction functional directly using the intrinsic conformable differential measure. Through fractional integration by parts and variational stationary conditions, we determine the optimal Lagrange multiplier. This derivation fundamentally confirms that the variational kernel inevitably yields the modified conformable fractional integral operator, while the recurrence formulation inherently satisfies the prescribed fractional initial conditions. The proposed algorithm circumvents computationally expensive convolution integrals and Gamma functions, relying exclusively on standard factorials. The proposed method is applied to different types of fractional problems, yielding closed-form series solutions that converge rapidly to the exact solutions. The results show the proposed algorithm's superior accuracy, simplicity, and computational efficiency.