Progress in Fractional Differentiation & Applications

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The theoretical study of fractional calculus has grown significantly during the last few years. For the theoretical analysis of fractional differential equations, primarily two methods were employed. One is the fixed point approach, which determines whether a solution exists, and the other is the functional analysis approach, which determines whether a solution is stable. This study investigates the theoretical features of HBV infection under a fractional operator with a nonsingular and nonlocal kernel. We examine the existence and uniqueness of the model’s results using the fixed point theorems of Banach and Krasnoselskii. According to the Hyres-Ulam stability studies, the HBV model’s solution is stable under the Atangana-Baleanu derivative.

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