Existence of solutions of boundary value problems for Caputo fractional differential equations on time scales

Authors

  • R. A. Yan School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, P R China
  • S. R. Sun School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, P R China
  • Z. L. Han School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, P R China
Abstract:

‎In this paper‎, ‎we study the boundary-value problem of fractional‎ ‎order dynamic equations on time scales‎, ‎$$‎ ‎^c{Delta}^{alpha}u(t)=f(t,u(t)),;;tin‎ ‎[0,1]_{mathbb{T}^{kappa^{2}}}:=J,;;1

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

existence of solutions of boundary value problems for caputo fractional differential equations on time scales

‎in this paper‎, ‎we study the boundary-value problem of fractional‎ ‎order dynamic equations on time scales‎, ‎$$‎ ‎^c{delta}^{alpha}u(t)=f(t,u(t)),;;tin‎ ‎[0,1]_{mathbb{t}^{kappa^{2}}}:=j,;;1

full text

Existence of triple positive solutions for boundary value problem of nonlinear fractional differential equations

This article is devoted to the study of existence and multiplicity of positive solutions to a class of nonlinear fractional order multi-point boundary value problems of the type−Dq0+u(t) = f(t, u(t)), 1 < q ≤ 2, 0 < t < 1,u(0) = 0, u(1) =m−2∑ i=1δiu(ηi),where Dq0+ represents standard Riemann-Liouville fractional derivative, δi, ηi ∈ (0, 1) withm−2∑i=1δiηi q−1 < 1, and f : [0, 1] × [0, ∞) → [0, ...

full text

Existence of positive solution to a class of boundary value problems of fractional differential equations

This paper is devoted to the study of establishing sufficient conditions for existence and uniqueness of positive solution to a class of non-linear problems of fractional differential equations. The boundary conditions involved Riemann-Liouville fractional order derivative and integral. Further, the non-linear function $f$ contain fractional order derivative which produce extra complexity. Than...

full text

On the existence and uniqueness of solution of initial value problem for fractional order differential equations on time scales

n this paper, at first the  concept of Caputo fractionalderivative is generalized on time scales. Then the fractional orderdifferential equations are introduced on time scales. Finally,sufficient and necessary conditions are presented for the existenceand uniqueness of solution of initial valueproblem including fractional order differential equations.

full text

On the existence of nonnegative solutions for a class of fractional boundary value problems

‎In this paper‎, ‎we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation‎. ‎By applying Kranoselskii`s fixed--point theorem in a cone‎, ‎first we prove the existence of solutions of an auxiliary BVP formulated by truncating the response function‎. ‎Then the Arzela--Ascoli theorem is used to take $C^1$ ...

full text

Solutions for some non-linear fractional differential equations with boundary value problems

In recent years, X.J.Xu [1] has been proved some results on mixed monotone operators.  Following the paper of X.J.Xu, we study the existence and uniqueness of the positive solutions for non-linear differential equations with boundary value problems. 

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 42  issue 2

pages  247- 262

publication date 2016-04-01

By following a journal you will be notified via email when a new issue of this journal is published.

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023