Abstract
Existence results for the three-point fractional boundary value problemDαx(t)=f(t,x(t),Dα−1x(t)),0<t<1,x(0)=A,x(η)−x(1)=(η−1)B,\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document} $$\\begin{aligned}& D^{\\alpha}x(t)= f \\bigl(t, x(t), D^{\\alpha-1} x(t) \\bigr),\\quad 0< t< 1, \\\\& x(0)=A, \\qquad x(\\eta)-x(1)=(\\eta-1)B, \\end{aligned}$$ \\end{document} are presented, where A, Binmathbb{R}, 0<eta<1, 1<alphaleq2. D^{alpha}x(t) is the conformable fractional derivative, and f: [0, 1]timesmathbb{R}^{2}tomathbb{R} is continuous. The analysis is based on the nonlinear alternative of Leray–Schauder.
Highlights
In recent years, due to the wide application in many engineering and scientific disciplines as the mathematical modeling of systems and processes in the fields of physics, chemistry, aerodynamics, electrodynamics of a complex medium, polymer rheology, etc., the fractional differential equations have been widely studied
Existence results for the three-point fractional boundary value problem
An extensive literature related to the existence of solutions of boundary value problems for fractional differential equations addressed by the use of various nonlinear functional analysis method
Summary
Due to the wide application in many engineering and scientific disciplines as the mathematical modeling of systems and processes in the fields of physics, chemistry, aerodynamics, electrodynamics of a complex medium, polymer rheology, etc., the fractional differential equations have been widely studied. Abstract Existence results for the three-point fractional boundary value problem Dαx(t) is the conformable fractional derivative, and f : [0, 1] × R2 → R is continuous. An extensive literature related to the existence of solutions of boundary value problems for fractional differential equations addressed by the use of various nonlinear functional analysis method.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
