An anti-periodic singular fractional differential problem of Lane-Emden type

Abstract

In this paper, we use both Riemann-Liouville integral and Caputo derivative to investigate a new nonlinear singular differential problem of Lane and Emden type. We note that for the studied singular problem, we will be concerned with some anti periodic conditions. So, we prove a first uniqueness result by application of Banach principle of contraction. Then, we prove a “second” existence result by application of Schaefer theorem. Two illustrative examples are discussed in details to show the applicability of the obtained results.

Subject Classification: (2010):

• 30C45
• 39B72
• 39B82

Keywords:

• Caputo derivative
• Lane and Emden equation
• Existence of solution
• Fractional equation