Browsing by Author "Trujillo, Juan J."

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Citation Count: Baleanu, Dumitru; Trujillo, Juan J.; Ahmad, Bashir, "Advanced Theoretical and Applied Studies of Fractional Differential Equations", Abstract and Applied Analysis, (2013)
Advanced Theoretical and Applied Studies of Fractional Differential Equations
(Hindawi Publishing Corporation, 2013) Baleanu, Dumitru; Trujillo, Juan J.; Ahmad, Bashir; 56389
Citation Count: Baleanu, Dumitru...et al. (2016). "Fractional calculus: Models and numerical methods: Second edition", Fractional Calculus: Models and Numerical Methods: Second Edition, Vol. 5, pp. 1-448.
Fractional calculus: Models and numerical methods: Second edition
(2016) Baleanu, Dumitru; Diethelm, Kai; Scalas, Enrico; Trujillo, Juan J.; 56389
This book will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods. Moreover, we will introduce some applied topics, in particular fractional variational methods which are used in physics, engineering or economics. We will also discuss the relationship between semi-Markov continuous-time random walks and the space-time fractional diffusion equation, which generalizes the usual theory relating random walks to the diffusion equation. These methods can be applied in finance, to model tick-by-tick (log)-price fluctuations, in insurance theory, to study ruin, as well as in macroeconomics as prototypical growth models. All these topics are complementary to what is dealt with in existing books on fractional calculus and its applications. This book will keep in mind the trade-off between full mathematical rigor and the needs of readers coming from different applied areas of science and engineering. In particular, the numerical methods listed in the book are presented in a readily accessible way that immediately allows the readers to implement them on a computer in a programming language of their choice. The second edition of the book has been expanded and now includes a discussion of additional, newly developed numerical methods for fractional calculus and a chapter on the application of fractional calculus for modeling processes in the life sciences. © 2017 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.
Citation Count: Baleanu, Dumitru; Trujillo, Juan J., "On exact solutions of a class of fractional Euler-Lagrange equations", Nonlinear Dynamics, Vol.52, No.4, pp.331-335, (2008).
On exact solutions of a class of fractional Euler-Lagrange equations
(Springer, 2008) Baleanu, Dumitru; Trujillo, Juan J.; 56389
In this paper, first a class of fractional differential equations are obtained by using the fractional variational principles. We find a fractional Lagrangian L(x(t), where D-c(a)t(alpha) x(t)) and 0 < alpha < 1, such that the following is the corresponding Euler-Lagrange D-t(b)alpha(D-c(a)t(alpha))x(t) + b(t, x(t)) ((c)(a)D(t)(alpha)x(t)) + f(t, x(t)) = 0. (1) At last, exact solutions for some Euler-Lagrange equations are presented. In particular, we consider the following equations D-t(b)alpha(D-c(a)t(alpha))x(t) = lambda x(t) (lambda is an element of R), (2) D-t(b)alpha(D-c(a)t(alpha))x(t) + g(t) D-c(a)t(alpha) x(t) = f(t), (3)