Author/Authors :
Zamir, Muhammad Department of Mathematics - University of Science and Technology - Banuu - Khyber Pakhtunkhwa, Pakistan , Shah, Kamal Department of Mathematics - University of Malakand - Khyber Pakhtunkhwa, Pakistan , Chohan, Muhammad Ikhlaq Department of Business Administration and Accounting - Al Buraimi University College - Muscat - Al‑Buraimi - Sultanate of Oman
Abstract :
The aims and objectives of this manuscript are concerned with the investigation of some appropriate conditions to establish existence theory of solutions to a class of nonlinear four-point boundary value problem (BVP) corresponding to fractional order differential equations (FODEs) provided as
{cDωy(t)=F(t,y(t),cDω−1y(t)),1<ω≤2,t∈J=[0,1],y(0)=ζy(α),y(1)=ξy(β),ξ, ζ, α,β∈(0,1),
where cDω is Caputo’s fractional derivative of order q and F∈(J×R×R,R) may be nonlinear. The required conditions are obtained by using classical results of functional analysis and fixed point theory. Further, we establish some adequate conditions for the Ulam–Hyers stability and generalized Ulam–Hyers stability for the solutions to the considered BVP of nonlinear FODEs. We include a proper problem to illustrate our established results.
