Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Editorial Citation - WoS: 2Citation - Scopus: 2Comment on "maxwell's Equations and Electromagnetic Lagrangian Density in Fractional Form" [J. Math. Phys. 53, 033505 ( 2012)](Amer inst Physics, 2014) Al-Jamel, A.; Widyan, H.; Baleanu, D.; Rabei, Eqab M.In a recent paper, Jaradat et al. [J. Math. Phys. 53, 033505 (2012)] have presented the fractional form of the electromagnetic Lagrangian density within the Riemann-Liouville fractional derivative. They claimed that the Agrawal procedure [O. P. Agrawal, J. Math. Anal. Appl. 272, 368 (2002)] is used to obtain Maxwell's equations in the fractional form, and the Hamilton's equations of motion together with the conserved quantities obtained from fractional Noether's theorem are reported. In this comment, we draw the attention that there are some serious steps of the procedure used in their work are not applicable even though their final results are correct. Their work should have been done based on a formulation as reported by Baleanu and Muslih [Phys. Scr. 72, 119 (2005)]. (C) 2014 AIP Publishing LLC.Conference Object Citation - WoS: 2Citation - Scopus: 1Invariant Investigation on the System of Hirota-Satsuma Coupled Kdv Equation(Amer inst Physics, 2018) Balmeh, Z.; Akgul, A.; Akgul, E. K.; Baleanu, D.; Hashemi, M. S.We show how invariant subspace method can be extended to the system time fractional differential equations and construct their exact solutions. Effectiveness of the method has been illustrated by the time fractional Hirota-Satsuma Coupled KdV(HSCKdV) equation.Article Citation - WoS: 26Citation - Scopus: 31Asymptotic Solutions of Fractional Interval Differential Equations With Nonsingular Kernel Derivative(Amer inst Physics, 2019) Ahmadian, A.; Salimi, M.; Ferrara, M.; Baleanu, D.; Salahshour, S.Realizing the behavior of the solution in the asymptotic situations is essential for repetitive applications in the control theory and modeling of the real-world systems. This study discusses a robust and definitive attitude to find the interval approximate asymptotic solutions of fractional differential equations (FDEs) with the Atangana-Baleanu (A-B) derivative. In fact, such critical tasks require to observe precisely the behavior of the noninterval case at first. In this regard, we initially shed light on the noninterval cases and analyze the behavior of the approximate asymptotic solutions, and then, we introduce the A-B derivative for FDEs under interval arithmetic and develop a new and reliable approximation approach for fractional interval differential equations with the interval A-B derivative to get the interval approximate asymptotic solutions. We exploit Laplace transforms to get the asymptotic approximate solution based on the interval asymptotic A-B fractional derivatives under interval arithmetic. The techniques developed here provide essential tools for finding interval approximation asymptotic solutions under interval fractional derivatives with nonsingular Mittag-Leffler kernels. Two cases arising in the real-world systems are modeled under interval notion and given to interpret the behavior of the interval approximate asymptotic solutions under different conditions as well as to validate this new approach. This study highlights the importance of the asymptotic solutions for FDEs regardless of interval or noninterval parameters. Published under license by AIP Publishing.Article Citation - WoS: 308Citation - Scopus: 338A New Fractional Model and Optimal Control of a Tumor-Immune Surveillance With Non-Singular Derivative Operator(Amer inst Physics, 2019) Jajarmi, A.; Sajjadi, S. S.; Mozyrska, D.; Baleanu, D.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.