Improvement of the Conformable Fractional Laplace Transform

—We investigate the conformable Laplace transform as an effective tool for solving fractional differential equations. As a case study, we consider a standard test equation and first solve it via the Riemann–Liouville (RL) definition. We then employ the conformable derivative to obtain an alternative solution. Finally, we apply the conformable Laplace transform and compare the three outcomes. The approaches are shown to agree, yielding the same closed-form solution, thereby highlighting the practicality and accuracy of the conformable Laplace transform for fractional initial-value problems.