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- W3159616396 abstract "Abstract This paper deals with the existence of nonnegative solutions for a class of boundary value problems of fractional q -differential equation ${}^{c}mathcal{D}_{q}^{sigma }[k](t) = w (t, k(t), {}^{c} mathcal{D}_{q}^{zeta }[k](t) )$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mmultiscripts> <mml:mi>D</mml:mi> <mml:mi>q</mml:mi> <mml:mi>σ</mml:mi> <mml:mprescripts /> <mml:none /> <mml:mi>c</mml:mi> </mml:mmultiscripts> <mml:mo>[</mml:mo> <mml:mi>k</mml:mi> <mml:mo>]</mml:mo> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>w</mml:mi> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>,</mml:mo> <mml:mi>k</mml:mi> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> <mml:mo>,</mml:mo> <mml:msup> <mml:mrow /> <mml:mi>c</mml:mi> </mml:msup> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mi>q</mml:mi> <mml:mi>ζ</mml:mi> </mml:msubsup> <mml:mo>[</mml:mo> <mml:mi>k</mml:mi> <mml:mo>]</mml:mo> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> <mml:mo>)</mml:mo> </mml:math> with three-point conditions for $t in (0,1)$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>t</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:math> on a time scale $mathbb{T}_{t_{0}}= { t : t =t_{0}q^{n}}cup {0}$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>T</mml:mi> <mml:msub> <mml:mi>t</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:msub> <mml:mo>=</mml:mo> <mml:mo>{</mml:mo> <mml:mi>t</mml:mi> <mml:mo>:</mml:mo> <mml:mi>t</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>t</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:msup> <mml:mi>q</mml:mi> <mml:mi>n</mml:mi> </mml:msup> <mml:mo>}</mml:mo> <mml:mo>∪</mml:mo> <mml:mo>{</mml:mo> <mml:mn>0</mml:mn> <mml:mo>}</mml:mo> </mml:math> , where $nin mathbb{N}$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>n</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>N</mml:mi> </mml:math> , $t_{0} in mathbb{R}$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>t</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>∈</mml:mo> <mml:mi>R</mml:mi> </mml:math> , and $0< q<1$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mn>0</mml:mn> <mml:mo><</mml:mo> <mml:mi>q</mml:mi> <mml:mo><</mml:mo> <mml:mn>1</mml:mn> </mml:math> , based on the Leray–Schauder nonlinear alternative and Guo–Krasnoselskii theorem. Moreover, we discuss the existence of nonnegative solutions. Examples involving algorithms and illustrated graphs are presented to demonstrate the validity of our theoretical findings." @default.
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- W3159616396 date "2021-04-23" @default.
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- W3159616396 title "The existence of nonnegative solutions for a nonlinear fractional q-differential problem via a different numerical approach" @default.
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- W3159616396 doi "https://doi.org/10.1186/s13660-021-02612-z" @default.
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