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Existence and uniqueness of nonlocal boundary conditions for Hilfer–Hadamard-type fractional differential equations
Advances in Difference Equations ( IF 3.1 ) Pub Date : 2021-04-07 , DOI: 10.1186/s13662-021-03358-0 Ahmad Y. A. Salamooni , D. D. Pawar
中文翻译:
Hilfer-Hadamard型分数阶微分方程非局部边界条件的存在与唯一性
更新日期:2021-04-08
Advances in Difference Equations ( IF 3.1 ) Pub Date : 2021-04-07 , DOI: 10.1186/s13662-021-03358-0 Ahmad Y. A. Salamooni , D. D. Pawar
In this paper, we use some fixed point theorems in Banach space for studying the existence and uniqueness results for Hilfer–Hadamard-type fractional differential equations
$$ {}_{\mathrm{H}}D^{\alpha ,\beta }x(t)+f\bigl(t,x(t)\bigr)=0 $$on the interval \((1,e]\) with nonlinear boundary conditions
$$ x(1+\epsilon )=\sum_{i=1}^{n-2}\nu _{i}x(\zeta _{i}),\qquad {}_{\mathrm{H}}D^{1,1}x(e)= \sum_{i=1}^{n-2} \sigma _{i}\, {}_{\mathrm{H}}D^{1,1}x( \zeta _{i}). $$中文翻译:
Hilfer-Hadamard型分数阶微分方程非局部边界条件的存在与唯一性
在本文中,我们使用Banach空间中的一些不动点定理来研究Hilfer-Hadamard型分数阶微分方程的存在性和唯一性结果
$$ {} _ {\ mathrm {H}} D ^ {\ alpha,\ beta} x(t)+ f \ bigl(t,x(t)\ bigr)= 0 $$在具有非线性边界条件的区间\((1,e] \)上
$$ x(1+ \ epsilon)= \ sum_ {i = 1} ^ {n-2} \ nu _ {i} x(\ zeta _ {i}),\ qquad {} _ {\ mathrm {H} } D ^ {1,1} x(e)= \ sum_ {i = 1} ^ {n-2} \ sigma _ {i} \,{} _ {\ mathrm {H}} D ^ {1,1 } x(\ zeta _ {i})。$$