Abstract
This paper is devoted to the research of some Caputo’s fractional derivative boundary value problems with a convection term. By the use of some fixed-point theorems and the properties of Green function, the existence results of at least one or triple positive solutions are presented. Finally, two examples are given to illustrate the main results.
Highlights
Fractional differential equations (FDEs) present new models for many applications in physics, biomathematics, environmental issues, control theory, image processing, chemistry, mechanics, and so on [1–17]
Researchers focus on studying various aspects of fractional differential equations, such as stability analysis, existence, multiplicity, and uniqueness of solutions [1–40]
The existence and multiplicity results of positive solutions represent a topic of high interest in fractional calculus
Summary
Fractional differential equations (FDEs) present new models for many applications in physics, biomathematics, environmental issues, control theory, image processing, chemistry, mechanics, and so on [1–17]. Researchers focus on studying various aspects of fractional differential equations, such as stability analysis, existence, multiplicity, and uniqueness of solutions [1–40]. Some authors studied the existence and uniqueness of solutions for fractional differential equations with Caputo or Riemann-Liouville derivatives based on the Banach contraction principle and investigate the stability results for various fractional problems [4, 5, 16, 17]. −RLDα0+y (x) + by (x) = f (t, y (t)) , x ∈ (0, 1) , [2] y (0) = y [1] = 0, where RLDα0+ is the Riemann-Liouville (R-L) fractional derivative, α ∈ [1, 2], and b > 0 They established an iterative scheme to approximate the unique positive solution under the singular conditions.
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