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Title: Existence and uniqueness of positive solutions to a class of singular integral boundary value problems of fractional order
Authors: Caballero, J. 
Harjani, J. 
Sadarangani, K. 
UNESCO Clasification: 120299 Otras (especificar)
120219 Ecuaciones diferenciales ordinarias
Keywords: Fixed point theorem
Fractional boundary value problem
Integral boundary conditions
Positive solution
Issue Date: 2023
Journal: Mediterranean Journal of Mathematics 
Abstract: In this paper, we are interested in the study of the existence and uniqueness of positive solutions to the nonlinear singular fractional differential equation D0+αu(t)+f(t,u(t),(Hu)(t))=0 with 0 < t< 1 , where D0+α denotes the classical Riemmann Liouville derivative, under the integral boundary conditions u(0) = u′(0) = ⋯ = u(n-2)(0) = 0 and u(1)=λ∫01u(s)ds, where λ∈ (0 , α) , H is an operator defined on C[0 , 1] into itself and f: (0 , 1] × [0 , ∞) × [0 , ∞) → [0 , ∞) is a continuous function which can have a singularity at (0, x, y). To state our results, we use a fixed point theorem recently proved. Finally, we present some examples illustrating the results obtained.
ISSN: 1660-5446
DOI: 10.1007/s00009-023-02294-5
Source: Mediterranean Journal of Mathematics [ISSN 1660-5446], v. 20 (2), (Abril 2023)
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