Fractional-order boundary value problem with Sturm-Liouville boundary conditions

Abstract

Using the new conformable fractional derivative, which differs from the Riemann-Liouville and Caputo fractional derivatives, we reformulate the second-order conjugate boundary value problem in this new setting. Utilizing the corresponding positive fractional Green's function, we apply a functional compression-expansion fixed point theorem to prove the existence of a positive solution. We then compare our results favorably to those based on the Riemann-Liouville fractional derivative.

12 pages, preprint. arXiv admin note: text overlap with arXiv:1411.5616

References in corpus (1)

• A New Fractional Derivative with Classical Properties

Cited by in corpus (2)

• Solutions around a Regular α Singular Point of a Sequential Conformable Fractional Differential Equation
• Existence of positive solutions for a class of conformable fractional differential equations with integral boundary conditions and a parameter