Reduction of order formula and fundamental set of solutions for linear fractional differential equations. (August 2018)

• Record Type: Journal Article
• Authors: Al-Refai, Mohammed
• Is Part Of: Applied mathematics letters. Volume 82(2018)
• Page Start: 8
• Page End: 13
• Publication Date: 2018-08
• Subjects: Fractional differential equations -- Caputo–Fabrizio fractional derivative -- Fundamental solutions set; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2018.02.014
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In this paper, we consider a class of linear fractional differential equations involving the Caputo–Fabrizio fractional derivative of order 1 < α < 2 . We derive, in closed form, a reduction of order formula to obtain a second linearly independent solution. We then establish a fundamental set of solutions result to the equation. One example is presented to illustrate the validity of the obtained results.