Solvability for a class of nonlocal singular fractional differential equations of Lane Emden type

Abstract

In this paper, we study a class of nonlocal singular differential equations of fractional orders. The considered class involves Caputo derivatives and Riemann-Liouville integral in its linearities. It is a more general problem for which the question of existence and uniqueness of solutions is investigated. For this class, the question of existence of at least one solution is also discussed. At the end, an illustrative example is presented.

Subject Classification: (2010):

• 30C45
• 39B72
• 39B82

Keywords:

• Caputo derivative
• Lane Emden equation
• Existence of solution
• Singular differential equation
• Nonlocal condition