Browsing by Author "Shiri, B."

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A Chebyshev spectral method based on operational matrix for fractional differential equations involving non-singular Mittag-Leffler kernel
(Springer, 2018) Baleanu, D.; Baleanu, Dumitru; Shiri, B.; Srivastava, H. M.; Al Qurashi, M.; 56389
In this paper, we solve a system of fractional differential equations within a fractional derivative involving the Mittag-Leffler kernel by using the spectral methods. We apply the Chebyshev polynomials as a base and obtain the necessary operational matrix of fractional integral using the Clenshaw-Curtis formula. By applying the operational matrix, we obtain a system of linear algebraic equations. The approximate solution is computed by solving this system. The regularity of the solution investigated and a convergence analysis is provided. Numerical examples are provided to show the effectiveness and efficiency of the method.
Applications of Short Memory Fractional Differential Equations with Impulses
(L and H Scientific Publishing, LLC, 2023) Shiri, B.; Baleanu, Dumitru; Wu, G.-C.; Baleanu, D.; 56389
Dynamical systems’ behavior is sometimes varied with some impulse and sudden changes in process. The dynamics of these systems can not be modeled by previous concepts of derivative or fractional derivatives any longer. The short memory concept is a solution and a better choice for fractional modeling of such processes. We apply short memory fractional differential equations for these systems. We propose collocation methods based on piecewise polynomials to approximate solutions of these equations. We provide various examples to demonstrate the application of the short memory derivative for impulse systems and efficiency of the presented numerical methods. © 2023 L&H Scientific Publishing, LLC. All rights reserved
Collocation methods for fractional differential equations involving non-singular kernel
(Pergamon-elsevier Science Ltd, 2018) Baleanu, D.; Baleanu, Dumitru; Shiri, B.; 56389
A system of fractional differential equations involving non-singular Mittag-Leffler kernel is considered. This system is transformed to a type of weakly singular integral equations in which the weak singular kernel is involved with both the unknown and known functions. The regularity and existence of its solution is studied. The collocation methods on discontinuous piecewise polynomial space are considered. The convergence and superconvergence properties of the introduced methods are derived on graded meshes. Numerical results provided to show that our theoretical convergence bounds are often sharp and the introduced methods are efficient. Some comparisons and applications are discussed. (C) 2018 Elsevier Ltd. All rights reserved.
Numerical solution of some fractional dynamical systems in medicine involving non-singular kernel with vector order
(Cankaya University, 2019) Shiri, B.; Baleanu, Dumitru; Baleanu, D.; 56389
In this paper, we propose systems of variable-order fractional equations for some problems in medicine. These problems include the dynamics of Zika virus fever and HIV infection of CD4+ T-cells. Two types of nonlocal fractional derivatives are considered and compared in these dynamics: The Liouville-Caputo’s definition and a definition involving non-singular Mittag-Leffler kernel. Predictor-corrector methods are described for simulating the corresponding dynamical systems. © 2019, Cankaya University. All rights reserved.
System of fractional differential algebraic equations with applications
(Pergamon-elsevier Science Ltd, 2019) Shiri, B.; Baleanu, Dumitru; Baleanu, D.; 56389
One of the important classes of coupled systems of algebraic, differential and fractional differential equations (CSADFDEs) is fractional differential algebraic equations (FDAEs). The main difference of such systems with other class of CSADFDEs is that their singularity remains constant in an interval. However, complete classifying and analyzing of these systems relay mainly to the concept of the index which we introduce in this paper. For a system of linear differential algebraic equations (DAEs) with constant coefficients, we observe that the solvability depends on the regularity of the corresponding pencils. However, we show that in general, similar properties of DAEs do not hold for FDAEs. In this paper, we introduce some practical applications of systems of FDAEs in physics such as a simple pendulum in a Newtonian fluid and electrical circuit containing a new practical element namely fractors. We obtain the index of introduced systems and discuss the solvability of these systems. We numerically solve the FDAEs of a pendulum in a fluid with three different fractional derivatives (Liouville-Caputo's definition, CaputoFabrizio's definition and with a definition with Mittag-Leffler kernel) and compare the effect of different fractional derivatives in this modeling. Finally, we solved some existing examples in research and showed the effectiveness and efficiency of the proposed numerical method. (C) 2019 Elsevier Ltd. All rights reserved.