Doi: http://dx.doi.org/10.15446/recolma.v48n2.54157

¹Universidad del Zulia, Maracaibo, Venezuela. Email: lgalue@hotmail.com

In recent years, there has been a great interest in fractional differential equations due to their frequent appearance in various fields, and their more accurate models of systems under consideration provided by fractional derivatives. In particular, fractional order telegraph equations have been considered and solved for many researchers, using different methods. In this paper we derived the solution of two homogeneous space-time fractional telegraph equations using the generalized differential transform method. The derivatives are considered in Caputo sense and the solutions are given in terms of generalized Mittag-Leffler function and the generalized Wright function. Further, various graphics are included which show the behavior of the solution obtained, and results given earlier by Momani, Odibat and Momani, Yildrim, Garg and Sharma, and Garg et al. are obtained as particular cases of ones our.

Key words: Fractional order telegraph equation, Generalized differential transform method, Caputo fractional derivative, Generalized Mittag-Leffler function, Generalized Wright function.

En los últimos años, ha habido un gran interés en las ecuaciones diferenciales fraccionales debido a su frecuente aparición en diversos campos, y a sus modelos más precisos de los sistemas en estudio proporcionados por las derivadas fraccionales. En particular, las ecuaciones telegráficas fraccionales han sido consideradas y resueltas por muchos investigadores, utilizando diferentes métodos. En este trabajo se derivó la solución de dos ecuaciones telegráficas homogéneas, con espacio-tiempo fraccionales, utilizando el método de la transformada diferencial generalizada. Las derivadas se consideran en el sentido Caputo y las soluciones se dan en términos de la función generalizada de Mittag-Leffler y la función de Wright generalizada. Además, se incluyen varias gráficas que muestran el comportamiento de la solución obtenida, y los resultados dados anteriormente por Momani, Odibat y Momani, Yildrim, Garg y Sharma, y Garg et al. se obtienen como casos particulares de los nuestros.

Palabras clave: Ecuación telegráfica de orden fraccional, método de la transformada diferencial generalizada, derivada fraccional de Caputo, función generalizada deMittag-Leffler, función de Wright generalizada.

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