Existence of Positive Solutions for N-term Non-autonomous Fractional Differential Equations |
| |
Authors: | Email author" target="_blank">A?BabakhaniEmail author Varsha?Daftardar-Gejji |
| |
Institution: | (1) Department of Mathematics, University of Pune, Ganeshkhind, Pune, 411007, India |
| |
Abstract: | Existence of positive solutions for the nonlinear fractional differential equation
D
αu = f(x,u), 0 < α < 1 has been given (S. Zhang. J. Math. Anal. Appl. 252 (2000), 804–812) where D
α denotes Riemann–Liouville fractional derivative. In the present work we extend this analysis for n-term non autonomous fractional
differential equations. We investigate existence of positive solutions for the following initial value problem
with initial conditions
where
is the standard Riemann–Liouville fractional derivative. Further the conditions on a
j
’s and f, under which the solution is (i) unique and (ii) unique and positive as well, are given |
| |
Keywords: | Riemann– Liouville fractional derivatives and integrals semi-ordered Banach space normal cone completely continuous operator equicontinuous set |
本文献已被 SpringerLink 等数据库收录! |
|