Abstract
In this manuscript, we obtain sufficient conditions required for the existence of solution to the following coupled system of nonlinear fractional order differential equations: <disp-formula id="Equa">D gamma omega (l)=F(l,omega(lambda l),upsilon(lambda l)),D delta upsilon (l)=F?</mml:mover>(l,omega(lambda l),upsilon(lambda l)),<graphic position="anchor" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13662_2020_2918_Article_Equa.gif"> </disp-formula> with fractional integral boundary conditions <disp-formula id="Equb">a1 omega (0)-b1 omega(eta)-c1 omega (1)=1 Gamma(gamma)integral 01</mml:msubsup>(1-rho)gamma -1 phi(rho,omega(rho))<mml:mspace width="0.2em"></mml:mspace>d rho <mml:mspace width="1em"></mml:mspace>anda2 upsilon (0)-b2 upsilon(xi)-c2 upsilon (1)=1 Gamma(delta)integral 01</mml:msubsup>(1-rho)delta -1 psi(rho,upsilon(rho))<mml:mspace width="0.2em"></mml:mspace>d rho,<graphic position="anchor" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13662_2020_2918_Article_Equb.gif"> </disp-formula> where l is an element of Z=[0,1], gamma,delta is an element of (0,1], 0<<1, D denotes the Caputo fractional derivative (in short CFD), F,F?</mml:mover>:ZxRxR -> R and phi,psi :ZxR -> R are continuous functions. The parameters eta, xi are such that 0<,xi <1, and ai,bi,ci (i=1,2) are real numbers with ai<not equal>bi+ci (i=1,2). Using topological degree theory, sufficient results are constructed for the existence of at least one and unique solution to the concerned problem. For the validity of our result, an appropriate example is presented in the end.