https://doi.org/10.1140/epjp/i2017-11341-0
Regular Article
On the solutions of fractional order of evolution equations
1
Faculty of Mathematics of Autonomous, University of Guerrero Chilpancingo, Guerrero, Mexico
2
CONACyT-Centro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, Mexico
* e-mail: jgomez@cenidet.edu.mx
Received:
17
December
2016
Accepted:
2
January
2017
Published online:
26
January
2017
In this paper we present a discussion of generalized Cauchy problems in a diffusion wave process, we consider bi-fractional-order evolution equations in the Riemann-Liouville, Liouville-Caputo, and Caputo-Fabrizio sense. Through Fourier transforms and Laplace transform we derive closed-form solutions to the Cauchy problems mentioned above. Similarly, we establish fundamental solutions. Finally, we give an application of the above results to the determination of decompositions of Dirac type for bi-fractional-order equations and write a formula for the moments for the fractional vibration of a beam equation. This type of decomposition allows us to speak of internal degrees of freedom in the vibration of a beam equation.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2017
