English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this article, we discuss a new Hadamard fractional differential system with four-point boundary conditions    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$\textstyle\begin{cases} {}^{H} D^{\alpha}u(t)+f(t,v(t))=l_{f},\quad t\in(1,e),\\ {}^{H} D^{\beta}v(t)+g(t,u(t))=l_{g},\quad t\in(1,e),\\ u^{(j)}(1)=v^{(j)}(1)=0, \quad 0\leq j\leq n-2,\\ u(e)=av(\xi),\qquad v(e)=bu(\eta),\quad \xi, \eta\in(1,e), \end{cases} $$\end{document}    {D    αH   u  (  t  )  +  f  (  t  ,  v  (  t  )  )  =   l  f   ,    t  ∈  (  1  ,  e  )  ,D    βH   v  (  t  )  +  g  (  t  ,  u  (  t  )  )  =   l  g   ,    t  ∈  (  1  ,  e  )  ,u   (  j  )    (  1  )  =   v   (  j  )    (  1  )  =  0  ,    0  ≤  j  ≤  n  −  2  ,u  (  e  )  =  a  v  (  ξ  )  ,    v  (  e  )  =  b  u  (  η  )  ,    ξ  ,  η  ∈  (  1  ,  e  )  ,where    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$a,b$\end{document}   a  ,  bare two parameters with    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$0< ab(\log\eta)^{\alpha-1}(\log\xi )^{\beta-1}<1$\end{document}   0  <  a  b    (  log  η  )    α  −  1(  log  ξ  )    β  −  1    <  1,    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$\alpha, \beta\in(n-1,n]$\end{document}   α  ,  β  ∈  (  n  −  1  ,  n  ]are two real numbers and    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$n\geq3$\end{document}   n  ≥  3,    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$f,g\in C([1,e]\times(-\infty,+\infty),(-\infty,+\infty))$\end{document}   f  ,  g  ∈  C  (  [  1  ,  e  ]  ×  (  −  ∞  ,  +  ∞  )  ,  (  −  ∞  ,  +  ∞  )  ),    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$l_{f}, l_{g}>0$\end{document}    l  f   ,   l  g   >  0are constants, and    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}${}^{H} D^{\alpha}, {}^{H} D^{\beta}$\end{document}    D    αH   ,H    D  βare the Hadamard fractional derivatives of fractional order. Based upon a fixed point theorem of increasing  φ -   \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$(h,r)$\end{document}   (  h  ,  r  )-concave operators, we establish the existence and uniqueness of solutions for the problem dependent on two constants    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$l_{f}, l_{g}$\end{document}    l  f   ,   l  g.

A uniqueness method to a new Hadamard fractional differential system with four-point boundary conditions