Russian Journal of Mathematical Physics

, Volume 14, Issue 3, pp 357-365

First online:

Explicit solutions of a certain class of differential equations by means of fractional calculus

  • H. M. SrivastavaAffiliated withDepartment of Mathematics and Statistics, University of Victoria Email author 
  • , Shy-Der LinAffiliated withDepartment of Applied Mathematics, Chung Yuan Christian University Chung-Li
  • , Yi-Ting ChaoAffiliated withDepartment of Applied Mathematics, Chung Yuan Christian University Chung-Li
  • , Pin-Yu WangAffiliated withDepartment of Mechanical Engineering, Nan-Ya Institute of Technology Chung-Li

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Judging by the remarkably large number of recent publications on Fractional Calculus and Its Applications in several widely diverse areas of mathematical, physical, and engineering sciences, the current popularity and importance of the subject of fractional calculus cannot be overemphasized. Motivated by some of these interesting developments, many authors have recently demonstrated the usefulness of fractional calculus in the derivation of explicit particular solutions of a number of linear ordinary and partial differential equations of the second and higher orders. The main object of the present paper is to show how several recent contributions on this subject, involving a certain class of ordinary differential equations, can be obtained (in a unified manner) by suitably applying some general theorems on explicit particular solutions of a family of linear ordinary fractional differintegral equations.