Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Existence of positive solutions for fractional differential systems with multi point boundary conditions

Existence of positive solutions for fractional differential systems with multi point boundary... In this paper, we study the existence of positive solutions to the boundary value problem for the fractional differential system $$\left\{\begin{array}{lll} D_{0^+}^\beta \phi_p(D_{0^+}^\alpha u) (t) = f_1 (t, u (t), v (t)),\quad t \in (0, 1),\\ D_{0^+}^\beta \phi_p(D_{0^+}^\alpha v) (t) = f_2 (t, u (t), v(t)), \quad t \in (0, 1),\\ D_{0^+}^\alpha u(0)= D_{0^+}^\alpha u(1)=0,\; u (0) = 0, \quad u (1)-\Sigma_{i=1}^{m-2} a_{1i}\;u(\xi_{1i})=\lambda_1,\\ D_{0^+}^\alpha v(0)= D_{0^+}^\alpha v(1)=0,\; v (0) = 0, \quad v (1)-\Sigma_{i=1}^{m-2} a_{2i}\; v(\xi_{2i})=\lambda_2, \end{array}\right. $$ where $${1<\alpha,\beta\leq 2, 2 <\alpha + \beta\leq 4, D_{0^+}^\alpha}$$ is the Riemann–Liouville fractional derivative of order α. By using the Leggett–Williams fixed point theorem in a cone, the existence of three positive solutions for nonlinear singular boundary value problems is obtained. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ANNALI DELL'UNIVERSITA' DI FERRARA Springer Journals

Existence of positive solutions for fractional differential systems with multi point boundary conditions

Download PDF
18 pages

Loading next page...
 
/lp/springer-journals/existence-of-positive-solutions-for-fractional-differential-systems-LhiThXNF1e
Publisher
Springer Journals
Copyright
Copyright © 2012 by Università degli Studi di Ferrara
Subject
Mathematics; Mathematics, general; Analysis; Geometry; History of Mathematical Sciences; Numerical Analysis; Algebraic Geometry
ISSN
0430-3202
eISSN
1827-1510
DOI
10.1007/s11565-012-0160-x
Publisher site
See Article on Publisher Site

Abstract

In this paper, we study the existence of positive solutions to the boundary value problem for the fractional differential system $$\left\{\begin{array}{lll} D_{0^+}^\beta \phi_p(D_{0^+}^\alpha u) (t) = f_1 (t, u (t), v (t)),\quad t \in (0, 1),\\ D_{0^+}^\beta \phi_p(D_{0^+}^\alpha v) (t) = f_2 (t, u (t), v(t)), \quad t \in (0, 1),\\ D_{0^+}^\alpha u(0)= D_{0^+}^\alpha u(1)=0,\; u (0) = 0, \quad u (1)-\Sigma_{i=1}^{m-2} a_{1i}\;u(\xi_{1i})=\lambda_1,\\ D_{0^+}^\alpha v(0)= D_{0^+}^\alpha v(1)=0,\; v (0) = 0, \quad v (1)-\Sigma_{i=1}^{m-2} a_{2i}\; v(\xi_{2i})=\lambda_2, \end{array}\right. $$ where $${1<\alpha,\beta\leq 2, 2 <\alpha + \beta\leq 4, D_{0^+}^\alpha}$$ is the Riemann–Liouville fractional derivative of order α. By using the Leggett–Williams fixed point theorem in a cone, the existence of three positive solutions for nonlinear singular boundary value problems is obtained.

Journal

ANNALI DELL'UNIVERSITA' DI FERRARA – Springer Journals

Published: Jun 26, 2012

References

  • Differential equations of fractional order: methods, results and problems I
    Kilbas, A.A.; Trujillo, J.J.
  • Differential equations of fractional order: methods, results and problems II
    Kilbas, A.A.; Trujillo, J.J.
  • Existence of positive solutions of nonlinear fractional differential equations
    Babakhani, A.; Gejji, V.D.
  • Existence and uniqueness for a nonlinear fractional differential equation
    Delbosco, D.; Rodino, L.
  • Anomalous transit-time dispersion in amorphous solids
    Scher, H.; Montroll, E.W.
  • Damping description involving fractional operators
    Gaul, L.; Klein, P.; Kemple, S.
  • A fractional calculus approach to self-semilar protein dynamics
    Glockle, W.G.; Nonnenmacher, T.F.
  • Fractals and Fractional calculus in continuum mechanics
    Mainardi, F
  • Relaxation in filled polymers: a fractional calculus approach
    Metzler, R.; Schick, W.; Kilian, H.G.; Nonnenmacher, T.F.L
  • Positive solutions for boundary value problem of nonlinear fractional differential equation
    Bai, Z.B.; Lü, H.S.
  • On the fractional order m-point boundary value problem in reflexive banach spaces and weak topologies
    Salem, H.A.H.
  • Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions
    Ahmad, B.; Nieto, J.
  • Positive solutions for three-point nonlinear fractional boundary value problems
    Saadi, A.; Benbachir, M.
  • General problem of the movement of a compressible fluid in a porous medium
    Leibenson L., S.
  • Antiperiodic solutions for Lienard-type differential equation with p-Laplacian operator
    Chen, T.; Liu, W.; Yang, C.
  • Upper and lower solution method and a singular boundary value problem for the one-dimensional p-Laplacian
    Jiang, D.; Gao, W.
  • The existence of solutions of m-point p-Laplacian boundary value problems at resonance
    Lian, L.; Ge, W.
  • On the existence of solutions for the periodic boundary value problems with p-Laplacian operator
    Liu, B.; Yu, J.
  • Multiple periodic solutions of p-Laplacian equation with one-side Nagumo condition
    Zhang, J.; Liu, W.; Ni, J.; Chen, T.
  • Fractional Integrals and Derivatives: Theory and Applications
    Samko, G.; Kilbas, A.; Marichev, O.
  • Fractional Differential Equations
    Podlubny, I.
  • Theory and Applications of Fractional Differential Equations
    Kilbas, A.A.; Srivastava, H.M.; Trujillo, J.J.
  • Multiple positive fixed points of nonlinear operators on ordered Banach spaces
    Leggett, R.W.; Williams, L.R.