Abstract
In this paper, we mainly discuss the existence and uniqueness results of solutions to fractional differential equations with multi-strip boundary conditions. When the fractional order α becomes integer, the existence theorem of positive solutions can be established by a monotone iterative technique. Also, some examples are presented to illustrate the main results.
Highlights
Differential equations attract many scholars’ interest since they can succinctly establish the relationship between variables and their derivatives
Fractional order calculus has been used as an important tool to improve mathematical modeling of many complex problems, such as in fluid mechanics, rheology, fractional model of nerve and fractional regression model; see [1,2,3,4,5], for instance
There are many achievements derived from some fractional equations with various boundary conditions, some recent contribution can be found in [6,7,8,9,10,11,12,13]
Summary
Differential equations attract many scholars’ interest since they can succinctly establish the relationship between variables and their derivatives. In [15], the authors considered the following equation with integral boundary conditions: Where Dα0+ is the Riemann–Liouville fractional derivative of order α, f : [0, 1] × R3 → R is a continuous function, 2 < α ≤ 3, 0 < β ≤ 1 < γ < α – 1, 0 < ξi ≤ 1, ai, bi are nonnegative constants satisfying ai ≥
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