Existence of the positive solutions for a tripled system of fractional differential equations via integral boundary conditions

Authors : Hojjat AFSHARİ, Hadi SHOJAAT, Mansoureh SİAHKALİ MORADİ

Pages : 186-199

Doi:10.53006/rna.938851

View : 14 | Download : 8

Publication Date : 2021-09-30

Article Type : Research Paper

Abstract :The purpose of this paper, is studying the existence and nonexistence of positive solutions to a class of a following tripled system of fractional differential equations. \begin{eqnarray*} \left\{ \begin{array}{ll} D^{\alpha}uinsert ignore into journalissuearticles values(\zeta);+ainsert ignore into journalissuearticles values(\zeta);finsert ignore into journalissuearticles values(\zeta,vinsert ignore into journalissuearticles values(\zeta);,\omegainsert ignore into journalissuearticles values(\zeta););=0, \quad \quad uinsert ignore into journalissuearticles values(0);=0,\quad uinsert ignore into journalissuearticles values(1);=\int_0^1\phiinsert ignore into journalissuearticles values(\zeta);uinsert ignore into journalissuearticles values(\zeta);d\zeta, \\ \\ D^{\beta}vinsert ignore into journalissuearticles values(\zeta);+binsert ignore into journalissuearticles values(\zeta);ginsert ignore into journalissuearticles values(\zeta,uinsert ignore into journalissuearticles values(\zeta);,\omegainsert ignore into journalissuearticles values(\zeta););=0, \quad \quad vinsert ignore into journalissuearticles values(0);=0,\quad vinsert ignore into journalissuearticles values(1);=\int_0^1\psiinsert ignore into journalissuearticles values(\zeta);vinsert ignore into journalissuearticles values(\zeta);d\zeta,\\ \\ D^{\gamma}\omegainsert ignore into journalissuearticles values(\zeta);+cinsert ignore into journalissuearticles values(\zeta);hinsert ignore into journalissuearticles values(\zeta,uinsert ignore into journalissuearticles values(\zeta);,vinsert ignore into journalissuearticles values(\zeta););=0,\quad \quad \omegainsert ignore into journalissuearticles values(0);=0,\quad \omegainsert ignore into journalissuearticles values(1);=\int_0^1\etainsert ignore into journalissuearticles values(\zeta);\omegainsert ignore into journalissuearticles values(\zeta);d\zeta,\\ \end{array} \right.\end{eqnarray*} \\ where $0\leq \zeta \leq 1$, $1<\alpha, \beta, \gamma \leq 2$, $a,b,c\in Cinsert ignore into journalissuearticles values(insert ignore into journalissuearticles values(0,1);,[0,\infty););$, $ \phi, \psi, \eta \in L^1[0,1]$ are nonnegative and $f,g,h\in Cinsert ignore into journalissuearticles values([0,1]\times[0,\infty);\times[0,\infty);,[0,\infty););$ and $D$ is the standard Riemann-Liouville fractional derivative.\\ Also, we provide some examples to demonstrate the validity of our results.
Keywords : Tripled System, fractional differential equation, integral boundary conditions, existence and nonexistence of positive solutions