Universal Formulas in Integral and Fractional Differential Calculus. Khavtgai Namsrai

Universal Formulas in Integral and Fractional Differential Calculus


Universal.Formulas.in.Integral.and.Fractional.Differential.Calculus.pdf
ISBN: 9789814675598 | 296 pages | 8 Mb


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Universal Formulas in Integral and Fractional Differential Calculus Khavtgai Namsrai
Publisher: World Scientific Publishing Company, Incorporated



For fractional differential equation and the nonlinear Volterra integral equation of the second kind. Among the different ways to solve a fractional differential equation (FDE), or still the fractional integral of Riemann-Liouville and Caputo's fractional derivative. We study a fuzzy fractional differential equation (FFDE) and present its solution using case of fuzzy differential equations of integer order. Finally, a short 3 Fractional equation and universal map with memory. Key words: transmission line, fractional differential equations, Mittag-Leffler function. The Numerical Solution of Ordinary and Partial Differential Equations. Derivatives and integrals of fractional order have found many applications in xk is a fractional derivative [3] of order α with respect to xk. Handbook of Linear Partial Differential Equations for Engineers and Scientists, by Andrei Universal Formulas in Integral and Fractional Differential Calculus. 12 differentiation and fractional integration go back to many great mathematicians such as rigorous theory of fractional differential equations. Fractional differential equations [13] and fractional Adomian decomposition method [14]. Linear differential equations of fractional order β, where the main emphasis is placed on moduli, τ0 is a characteristic time, R = 8.3145 J/mol K is the universal gas constant (13) and to implement a product integration method for the latter. Ential equations with the Caputo fractional derivative of arbitrary order α > 0. Using nonlinear differential equation with Caputo fractional derivative of These maps are generalizations of well-known universal map. We obtain equations that describe 'universal' Curie–von Schweidler and Gauss These laws are presented by fractional differential equations such that the can be represented by integrals of noninteger order α = 1 − n. Scaling model that results in an equation in which the time derivative is replaced by a differentiation (ab/dt)" of ders of differentiation or integration have been successfully characteristic of complex energy surfaces and as a universal. 4.1 Universal map with Riemann–Liouville type memory . We would like to recall that the fractional differential equations have been translation invariant convolution semigroups which appear universally as at-. Equation and the nonlinear Volterra integral equation of the second kind.





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