Laplace transform for solving some families of fractional differential equations and its applications

• Published in: Advances in difference equations Vol. 2013; no. 1; p. 137
• Main Authors: Lin, Shy-Der, Lu, Chia-Hung
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 13.05.2013; BioMed Central Ltd
• Subjects: Analysis; Difference and Functional Equations; Functional Analysis; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; Proceedings of the International Congress in Honour of Professor Hari M. Srivastava; Laplace transform of the fractional derivative; Wright function; Riemann-Liouville fractional integrals; fractional-order differential equations; Mittag-Leffler function; gamma function
• ISSN: 1687-1847; 1687-1847
• DOI: 10.1186/1687-1847-2013-137

In many recent works, many authors have demonstrated the usefulness of fractional calculus in the derivation of particular solutions of a significantly large number of linear ordinary and partial differential equations of the second and higher orders. The main objective of the present paper is to show how this simple fractional calculus method to the solutions of some families of fractional differential equations would lead naturally to several interesting consequences, which include (for example) a generalization of the classical Frobenius method. The methodology presented here is based chiefly upon some general theorems on (explicit) particular solutions of some families of fractional differential equations with the Laplace transform and the expansion coefficients of binomial series. MSC: 26A33, 33C10, 34A05.