Browsing by Author "Sajjadi, S. S."

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Citation Count: Jajarmi, A...et al. (2017). "A New Feature of the Fractional Euler–Lagrange Equations for A Coupled Oscillator Using A Nonsingular Operator Approach", Frontiers in Physics, Vol. 7.
A New Feature of the Fractional Euler–Lagrange Equations for A Coupled Oscillator Using A Nonsingular Operator Approach
(Frontiers Media S.A., 2019) Jajarmi, Amin; Baleanu, Dumitru; Sajjadi, S. S.; Asad, Jihad H.; 56389
In this new work, the free motion of a coupled oscillator is investigated. First, a fully description of the system under study is formulated by considering its classical Lagrangian, and as a result, the classical Euler–Lagrange equations of motion are constructed. After this point, we extend the classical Lagrangian in fractional sense, and thus, the fractional Euler–Lagrange equations of motion are derived. In this new formulation, we consider a recently introduced fractional operator with Mittag–Leffler non-singular kernel. We also present an efficient numerical method for solving the latter equations in a proper manner. Due to this new powerful technique, we are able to obtain remarkable physical thinks; indeed, we indicate that the complex behavior of many physical systems is realistically demonstrated via the fractional calculus modeling. Finally, we report our numerical findings to verify the theoretical analysis. © Copyright © 2019 Jajarmi, Baleanu, Sajjadi and Asad.
Citation Count: Baleanu, D...et al. (2019). "A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator", Chaos, Vol. 29, No. 8.
A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator
(Amer Inst Physics, 2019) Baleanu, Dumitru; Jajarmi, Amin; Sajjadi, S. S.; Mozyrska, D.; 56389
In this paper, we present a new fractional-order mathematical model for a tumor-immune surveillance mechanism. We analyze the interactions between various tumor cell populations and immune system via a system of fractional differential equations (FDEs). An efficient numerical procedure is suggested to solve these FDEs by considering singular and nonsingular derivative operators. An optimal control strategy for investigating the effect of chemotherapy treatment on the proposed fractional model is also provided. Simulation results show that the new presented model based on the fractional operator with Mittag-Leffler kernel represents various asymptomatic behaviors that tracks the real data more accurately than the other fractional- and integer-order models. Numerical simulations also verify the efficiency of the proposed optimal control strategy and show that the growth of the naive tumor cell population is successfully declined. Published under license by AIP Publishing.