In this paper, we develop time fractional Hepatitis B model and analyze qualitatively. The Caputo fractional derivative operator of order α ∈ (0, 1] is employed to obtain the system of fractional differential equations. The stability and sensitivity analysis of fractional order model has been made and verify the non-negative unique solution. LADM was successfully used for solving different problems. Laplace transform method is a useful technique in different field of biological science,

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... ing and applied mathematics. The latest technique (LADM) is employed on the developed fractional order model for numerical solutions. Finally, numerical simulations are also established to investigate the influence of the system parameter on the spread of the disease and which show the effect of fractional parameter α on our obtained solutions.