Fractional order epidemic model Fractional SIS model Fractional forward euler method Variational iteration method Mittag leffler function a b s t r a c tWe consider the fractional order epidemic model based on assumption that people will recover after disease and may be infected again on a time interval of non fatal disease. Our mathematical formulation is based on the fractional Caputo derivative. The existence and uniqueness of the solution is discussed. Furthermore, numerical solution is studied by variational iteration method and Euler method. Consequently, some numerical results are presented within.

In this paper, a class of fractional order differential equation expressed with Atangana–Baleanu Caputo derivative with nonlinear term is discussed. The existence and uniqueness of the solution of the general fractional differential equation are expressed. To present numerical results, we construct approximate scheme to be used for producing numerical solutions of the considered fractional differential equation. As an illustrative numerical example, we consider two Riccati fractional differential equations with different derivatives: Atangana–Baleanu Caputo and Caputo derivatives. Finally, the study of those examples verifies the theoretical results of global existence and uniqueness of solution. Moreover, numerical results underline the difference between solutions of both examples.

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In this paper, we introduce a fractional order into a psoriasis model. The system is composed of two fractional equations; we prove the local existence and uniqueness of the solution of the fractional psoriasis system; some stability conditions of the model equilibrium are given; finally, we further present some numerical results that confirm the stability.

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