In the last decade, the theory of local fractional calculus has been successfully used to describe and solve fundamental science and engineering problems. In this article, the local fractional Yang-Laplace variational iteration method has been used for solving the local More
In the last decade, the theory of local fractional calculus has been successfully used to describe and solve fundamental science and engineering problems. In this article, the local fractional Yang-Laplace variational iteration method has been used for solving the local fractional partial differential equation on a cantor set. The non-differentiable exact and approximate solutions are obtained for kind of local fractional linear and nonlinear equations. It is shown that the used method is an efficient and easy method to implement for linear and nonlinear problems arising in science and engineering. In this article, we emphasize on the LFYLVM method which is a combination form of local fractional variational iteration method and Yang-Laplace transform. Most of the obtained solutions from this method are in series form that converge rapidly to exact or approximate solutions. Illustrative examples demonstrate that the method is able to reduce the volume of computation compared to the existing classical methods.
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In this paper, a hybrid function method based on combination of block-pulse functions and Legendre polynomials is used for solving a fractional model of HIV infection of CD4+ T cells in which fractional derivatives are considered in Caputo sense. Using this method, the More
In this paper, a hybrid function method based on combination of block-pulse functions and Legendre polynomials is used for solving a fractional model of HIV infection of CD4+ T cells in which fractional derivatives are considered in Caputo sense. Using this method, the system of fractional ordinary differential equations which is the mathematical model for the fractional model of HIV infection of CD4+T cells, is reduced into a system of algebraic equations. This system can be solved by a numerical method. Also, convergence analysis of the method is studied and an upper bound of the error is obtained. To show efficiency and accuracy the proposed method, a numerical example is simulated and some comparisons and results are reported. In this paper, a hybrid function method based on combination of block-pulse functions and Legendre polynomials is used for solving a fractional model of HIV infection of CD4+ T cells in which fractional derivatives are considered in Caputo sense. Using this method, the system of fractional ordinary differential equations which is the mathematical model for the fractional model of HIV infection of CD4+T cells, is reduced into a system of algebraic equations. This system can be solved by a numerical method. Also, convergence analysis of the method is studied and an upper bound of the error is obtained. To show efficiency and accuracy the proposed method, a numerical example is simulated and some comparisons and results are reported.
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The quantum calculus or q-calculus begins with F. H. Jackson in the early twentieth century, but only recently it has aroused interest, due to high demand of mathematics that is modeling quantum computing and it has been an important subject for applied sciences . The q More
The quantum calculus or q-calculus begins with F. H. Jackson in the early twentieth century, but only recently it has aroused interest, due to high demand of mathematics that is modeling quantum computing and it has been an important subject for applied sciences . The quantum calculus is one of the applied and inter disciplinary sciences, which is more important than the classical calculus because in the standard calculus the definition of the derivative depends on the existence of limit but the quantum derivative in quantum calculus works without the definition of limit and for this reason the work with a quantum calculus is numerically faster and easier than the standard calculus. In this paper, fuzzy quantum derivative, fuzzy quantum fractional derivative in Caputo sense by using generalized Hukuhara difference and fuzzy quantum fractional integral of the Riemann-Liouville type are introduced, then the related theorems and properties are provided in details.These results occur in many applications as physics, quantum theory, number theory, statistical mechanics, etc.
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In this work, we have applied Elzaki transform and He's homotopy perturbation method to solvepartial dierential equation (PDEs) with time-fractional derivative. With help He's homotopy per-turbation, we can handle the nonlinear terms. Further, we have applied this sugg More
In this work, we have applied Elzaki transform and He's homotopy perturbation method to solvepartial dierential equation (PDEs) with time-fractional derivative. With help He's homotopy per-turbation, we can handle the nonlinear terms. Further, we have applied this suggested He's homotopyperturbation method in order to reformulate initial value problem. Some illustrative examples aregiven in order to show the ability and simplicity of the approach. All numerical calculations in thismanuscript were performed on a PC applying some programs written in Maple.
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Here we research the univariate fuzzy ordinary and fractional quantitative approximation of fuzzy real valued functions on a compact interval by quasi-interpolation general sigmoid activation function relied on fuzzy neural network operators. These approximations are de More
Here we research the univariate fuzzy ordinary and fractional quantitative approximation of fuzzy real valued functions on a compact interval by quasi-interpolation general sigmoid activation function relied on fuzzy neural network operators. These approximations are derived by establishing fuzzy Jackson type inequalities involving the fuzzy moduli of continuity of the function, or of the right and left Caputo fuzzy fractional derivatives of the involved function. The approximations are fuzzy pointwise and fuzzy uniform. The related feed-forward
fuzzy neural networks are with one hidden layer. We study in particular the fuzzy integer derivative and just fuzzy continuous cases. Our fuzzy fractional approximation result using higher order fuzzy differentiation converges better than in the fuzzy just continuous case.
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بـه دسـت آوردن راه حـل تحلیلـی یا عددی معادلات دیفرانسـیل کسـری بـه ویژه در سـال هـای اخیر ،یکی از مسـائل مشـکل و چالـش برانگیز در میـان ریاضیدانان و مهندسـان اسـت.هدف از ایـن مقالـه توسـعه روش تقـارن لی برای حـل معادلات دیفرانسـیل جزئی مرتبه دوم بر اسـاس مشـتق کسـری قا More
بـه دسـت آوردن راه حـل تحلیلـی یا عددی معادلات دیفرانسـیل کسـری بـه ویژه در سـال هـای اخیر ،یکی از مسـائل مشـکل و چالـش برانگیز در میـان ریاضیدانان و مهندسـان اسـت.هدف از ایـن مقالـه توسـعه روش تقـارن لی برای حـل معادلات دیفرانسـیل جزئی مرتبه دوم بر اسـاس مشـتق کسـری قابل انطباق اسـت. برخی از نمونـه هـای عددی برای نشـان دادن رویکرد پیشـنهادی ارائه شـده اسـت.
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در مقاله حاضر، تکنیک آبل برای یافتن جواب عمومی از معادلات دیفرانسیل معمولی مرتبه اول خطی اصلاح شده با مشتق M-کسری کوتاه شده، توسعه داده شده است. با استفاده از روش پیشنهادی، جواب عمومی دو معادله دیفرانسیل معمولی مرتبه اول غیرخطی شناخته شده، برنولی و ریکاتی، برمبنای مشتق More
در مقاله حاضر، تکنیک آبل برای یافتن جواب عمومی از معادلات دیفرانسیل معمولی مرتبه اول خطی اصلاح شده با مشتق M-کسری کوتاه شده، توسعه داده شده است. با استفاده از روش پیشنهادی، جواب عمومی دو معادله دیفرانسیل معمولی مرتبه اول غیرخطی شناخته شده، برنولی و ریکاتی، برمبنای مشتق M-کسری کوتاه شده به دست آمده است. برای هر معادله، چند مثال برای رضایتبخشی و کارایی روش پیشنهادی ارائه شده است.
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In this research, differential quadrature radial basis functions Method is performed to a fractional order model of HIV infection of CD4+T. Here, Caputo fractional derivative is used and it is approximated by forward finite difference method. Results have been compared More
In this research, differential quadrature radial basis functions Method is performed to a fractional order model of HIV infection of CD4+T. Here, Caputo fractional derivative is used and it is approximated by forward finite difference method. Results have been compared with the results of Laplace Adomian decomposition method (LADM), Laplace Adomian decomposition method-pade (LADM-pade), Runge-Kutta, Variational iteration method (VIM) and Variational iteration method-pade (VIM-Pade) for α_1=α_2=α_3 and residual functions have been plotted. And also approximate solutions of suggested method for different order of fractional derivatives have been shown.
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