Abstract
This paper investigates the existence and multiplicity of positive solutions for a class of higher-order nonlinear fractional differential equations with integral boundary conditions. The results are established by converting the problem into an equivalent integral equation and applying Krasnoselskii's fixed-point theorem in cones. The nonexistence of positive solutions is also studied.
Highlights
Fractional differential equations arise in many engineering and scientific disciplines as the mathematical modelling of systems and processes in the fields of physics, chemistry, aerodynamics, electrodynamics of complex medium, polymer rheology, Bode’s analysis of feedback amplifiers, capacitor theory, electrical circuits, electron-analytical chemistry, biology, control theory, fitting of experimental data, and so forth, and involves derivatives of fractional order
In 23, Zhang used a fixed-point theorem for the mixed monotone operator to show the existence of positive solutions to the following singular fractional differential equation
By using the famous Guo-Krasnoselskii fixed-point theorem, we have investigated the existence and multiplicity of positive solutions for a class of higher-order nonlinear fractional differential equations with integral boundary conditions and obtained some verifiable sufficient criteria
Summary
Fractional differential equations arise in many engineering and scientific disciplines as the mathematical modelling of systems and processes in the fields of physics, chemistry, aerodynamics, electrodynamics of complex medium, polymer rheology, Bode’s analysis of feedback amplifiers, capacitor theory, electrical circuits, electron-analytical chemistry, biology, control theory, fitting of experimental data, and so forth, and involves derivatives of fractional order. In 23 , Zhang used a fixed-point theorem for the mixed monotone operator to show the existence of positive solutions to the following singular fractional differential equation. Motivated by the above mentioned work, we study the following higher-order singular boundary value problem of fractional differential equation. N − 2, the boundary value problems P is related to a m-point boundary value problems of integerorder differential equation Under this case, a great deal of research has been devoted to the existence of solutions for problem P , for example, see Pang et al , Yang and Wei. , Feng and Ge , and references therein. I0α D0α u t u t C1tα−1 C2tα−2 · · · CN tα−N , 1.8 for some Ci ∈ R, i 1, 2, . . . , N, where N is the smallest integer greater than or equal to α
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