Particular solutions of a certain class of associated Cauchy-Euler fractional partial differential equations via fractional calculus

• Published in: Boundary value problems Vol. 2013; no. 1; p. 126
• Main Authors: Lin, Shy-Der, Lu, Chia-Hung, Su, Shou-Mei
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 16.05.2013; BioMed Central Ltd
• Subjects: Analysis; Approximations and Expansions; Difference and Functional Equations; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; Proceedings of the International Congress in Honour of Professor Hari M. Srivastava; fractional calculus; differential equation; index law; linearity property; generalized Leibniz rule; analytic function; initial and boundary value; partial differential equation; principle value
• ISSN: 1687-2770; 1687-2770
• DOI: 10.1186/1687-2770-2013-126

In recent years, various operators of fractional calculus (that is, calculus of integrals and derivatives of arbitrary real or complex orders) have been investigated and applied in many remarkably diverse fields of science and engineering. Many authors have demonstrated the usefulness of fractional calculus in the derivation of particular solutions of a number of linear ordinary and partial differential equations of the second and higher orders. The purpose of this paper is to present a certain class of the explicit particular solutions of the associated Cauchy-Euler fractional partial differential equation of arbitrary real or complex orders and their applications as follows: where u = u ( x , t ) ; A , B , C , M , N , α and β are arbitrary constants. MSC: 26A33, 33C10, 34A05.