On the existence of nonnegative solutions of nonlocal boundary value problems for a class of fractional differential equations

Babakhani, Abolfazl

doi:10.5899/2012/jnaa-00164

Journal of Nonlinear Analysis and Application

2012

DOI: 10.5899/2012/jnaa-00164

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On the existence of nonnegative solutions of nonlocal boundary value problems for a class of fractional differential equations

Abolfazl Babakhani¹

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2021

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Multiple solutions for a class of boundary value problems of fractional differential equations with generalized Caputo derivatives

Li¹,

Liu

2021

MATH

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<abstract>This paper is mainly concerned with the existence of multiple solutions for the following boundary value problems of fractional differential equations with generalized Caputo derivatives: <disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \hskip 3mm \left\{ \begin{array}{lll} ^{C}_{0}D^{\alpha}_{g}x(t)+f(t, x) = 0, \ 0<t<1;\\ x(0) = 0, \ ^{C}_{0}D^{1}_{g}x(0) = 0, \ ^{C}_{0}D^{\nu}_{g}x(1) = \int_{0}^{1}h(t)^{C}_{0}D^{\nu}_{g}x(t)g'(t)dt, \end{array}\right. $\end{document} </tex-math></disp-formula> where $ 2 < \alpha < 3 $, $ 1 < \nu < 2 $, $ \alpha-\nu-1 > 0 $, $ f\in C([0, 1]\times \mathbb{R}^{+}, \mathbb{R}^{+}) $, $ g' > 0 $, $ h\in C([0, 1], \mathbb{R}^{+}) $, $ \mathbb{R}^{+} = [0, +\infty) $. Applying the fixed point theorem on cone, the existence of multiple solutions for considered system is obtained. The results generalize and improve existing conclusions. Meanwhile, the Ulam stability for considered system is also considered. Finally, three examples are worked out to illustrate the main results.</abstract>

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Multiple solutions for a class of boundary value problems of fractional differential equations with generalized Caputo derivatives

Li¹,

Liu

2021

MATH

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On the existence of nonnegative solutions of nonlocal boundary value problems for a class of fractional differential equations

Cited by 1 publication

References 31 publications

Multiple solutions for a class of boundary value problems of fractional differential equations with generalized Caputo derivatives

Multiple solutions for a class of boundary value problems of fractional differential equations with generalized Caputo derivatives

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