Abstract
In this work, we study some types of Ulam stability for a nonlinear fractional differential equation of Lane–Emden type with anti periodic conditions. Then, by using a numerical approach for the Caputo derivative, we investigate behaviors of the considered problem.
Highlights
The theory of singular fractional boundary value problems has become an area of research investigation in the last three decades
One of the equations describing this type of problems is the very important Lane–Emden equation, which was published by Lane in 1870 [18] and detailed by Emden [8]
⎪⎪⎩ky(>0)0=, 0, y(1) = b η 0 y(s) ds, 0 < η < 1, Iqy(u) = y(1), 0 < u < 1, 0 < λ ≤ 1, 1 ≤ β ≤ 2, 0 ≤ α, δ ≤ 1, t ∈ ]0, 1[, Motivated by the above cited papers, in [25] we have proved the existence and uniqueness of solutions by application of the Banach contraction principle for the following anti periodic fractional differential problem:
Summary
The theory of singular fractional boundary value problems has become an area of research investigation in the last three decades (see [1, 3, 6, 7, 16, 21]). In [20], the authors have used the method of collocation to study the following Lane–Emden problem: ⎩k ≥ 0, 1 < α ≤ 2, 0 < β ≤ 1, t ∈ [0, 1], Ibrahim [15] has been concerned with the stability of Ulam Hyers for the following fractional Lane–Emden problem:
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