Juan J. Trujillo

Bio: Juan J. Trujillo is an academic researcher from University of La Laguna. The author has contributed to research in topics: Fractional calculus & Nonlinear system. The author has an hindex of 39, co-authored 156 publications receiving 18141 citations. Previous affiliations of Juan J. Trujillo include Spanish National Research Council.

Theory and Applications of Fractional Differential Equations

Abstract: 1. Preliminaries. 2. Fractional Integrals and Fractional Derivatives. 3. Ordinary Fractional Differential Equations. Existence and Uniqueness Theorems. 4. Methods for Explicitly solving Fractional Differential Equations. 5. Integral Transform Methods for Explicit Solutions to Fractional Differential Equations. 6. Partial Fractional Differential Equations. 7. Sequential Linear Differential Equations of Fractional Order. 8. Further Applications of Fractional Models. Bibliography Subject Index

Fractional Calculus: Models and Numerical Methods

Abstract: Survey of Numerical Methods to Solve Ordinary and Partial Fractional Differential Equations Specific and Efficient Methods to Solve Ordinary and Partial Fractional Differential Equations Fractional Variational Principles Continuous-Time Random Walks (CTRWs) Applications to Finance and Economics Generalized Stirling Numbers of First and Second Kind in the Framework of Fractional Calculus.

Differential equations of fractional order:methods results and problem —I

Abstract: Thc paper deals with the so-called differential equations of fractional order in which an unknown function is contained under the operation of a derivative of fractional order. A survey of the methods and results in the theory of such ordinary fractional differential equations is given. In particular, the method based on the reduction of the Cauchy-type problem for the fractional differential equations to the Volterra integral equations is discussed, and the Laplace transform, operational calculas compositional methods for the solution of linear differential equations of fractional order are presented. Problems and new trends of research are discussed.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

A new Definition of Fractional Derivative without Singular Kernel

Abstract: In the paper, we present a new definition of fractional deriva tive with a smooth kernel which takes on two different representations for the temporal and spatial variable. The first works on the time variables; thus it is suitable to use th e Laplace transform. The second definition is related to the spatial va riables, by a non-local fractional derivative, for which it is more convenient to work with the Fourier transform. The interest for this new approach with a regular kernel was born from the prospect that there is a class of non-local systems, which have the ability to descri be the material heterogeneities and the fluctuations of diff erent scales, which cannot be well described by classical local theories or by fractional models with singular kernel.