Stability and existence results for a class of nonlinear fractional differential equations with singularity. (8th November 2018)

• Record Type: Journal Article
• Authors: Alkhazzan, Abdulwasea; Jiang, Peng; Baleanu, Dumitru; Khan, Hasib; Khan, Aziz
• Other Names: Anguelov Roumen guestEditor.; Banasiak Jacek guestEditor.; Debbouche Amar guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 18(2018)
• Page Start: 9321
• Page End: 9334
• Publication Date: 2018-11-08
• Subjects: Caputo fractional derivative -- existence of positive solution -- Hyers‐Ulam stability -- Riemann‐Liouville fractional derivative -- singular fractional differential equations; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5263
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we are dealing with an analytical study of a singular fractional order nonlinear differential equation with fractional integral and differential boundary conditions and ϕ p ‐operator, for existence and stability results. Our problem is based on two types of fractional order derivatives, that is, Caputo factional derivative of order σ and Riemann‐Liouville derivative of order β, where m − 1 < σ, β ≤ m, and m ∈ {3, 4, 5, …}. The suggested problem will be converted into an equivalent integral form by the help of Green function. After the proofs for these properties, some classical fixed point theorems are employed for the existence of positive solution (EPS). For application of the results, an expressive example is included.