Existence and Uniqueness of Solutions for the System of Nonlinear Fractional Differential Equations with Nonlocal and Integral Boundary Conditions

In the present study, the nonlocal and integral boundary value problems for the system of nonlinear fractional differential equations involving the Caputo fractional derivative are investigated. Theorems on existence and uniqueness of a solution are established under some sufficient conditions on nonlinear terms. A simple example of application of the main result of this paper is presented.

[1]  Landong Liu,et al.  Existence of solution for boundary value problem of nonlinear fractional differential equation , 2007 .

[2]  Bashir Ahmad,et al.  Existence Results for Nonlinear Boundary Value Problems of Fractional Integrodifferential Equations with Integral Boundary Conditions , 2009 .

[3]  Rabha W. Ibrahim,et al.  On the existence and uniqueness of solutions of a class of fractional differential equations , 2007 .

[4]  Ravi P. Agarwal,et al.  On the Existence of Equilibrium Points, Boundedness, Oscillating Behavior and Positivity of a SVEIRS Epidemic Model under Constant and Impulsive Vaccination , 2011 .

[5]  Ravi P. Agarwal,et al.  Weighted pseudo-almost periodic solutions of a class of semilinear fractional differential equations , 2010 .

[6]  Chengjun Yuan,et al.  Two positive solutions for (n − 1, 1)-type semipositone integral boundary value problems for coupled systems of nonlinear fractional differential equations☆ , 2012 .

[7]  Keith B. Oldham,et al.  Fractional differential equations in electrochemistry , 2010, Adv. Eng. Softw..

[8]  A. Rousan,et al.  POTENTIALS OF ARBITRARY FORCES WITH FRACTIONAL DERIVATIVES , 2004 .

[9]  C. Yuan.  MULTIPLE POSITIVE SOLUTIONS FOR SEMIPOSITONE (n, p)-TYPE BOUNDARY VALUE PROBLEMS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS , 2011 .

[10]  Abdelkader Boucherif,et al.  Second-order boundary value problems with integral boundary conditions , 2009 .

[11]  M. de La Sen,et al.  About Robust Stability of Caputo Linear Fractional Dynamic Systems with Time Delays through Fixed Point Theory , 2011 .

[12]  R. Magin.  Fractional Calculus in Bioengineering , 2006 .

[13]  Mouffak Benchohra,et al.  BOUNDARY VALUE PROBLEMS FOR DIFFERENTIAL EQUATIONS WITH FRACTIONAL ORDER , 2008 .

[14]  J. Henderson,et al.  EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH INTEGRAL BOUNDARY CONDITIONS , 2011 .

[15]  José António Tenreiro Machado,et al.  Fractional signal processing and applications , 2003, Signal Process..

[16]  Manuel Ortigueira,et al.  Special Issue on Fractional signal Processing and applications , 2003 .

[17]  R. Agarwal,et al.  A Survey on Existence Results for Boundary Value Problems of Nonlinear Fractional Differential Equations and Inclusions , 2010 .

[18]  Om P. Agrawal,et al.  Formulation of Euler–Lagrange equations for fractional variational problems , 2002 .

[19]  Multiple positive solutions for (n-1, 1)-type semipositone conjugate boundary value problems for coupled systems of nonlinear fractional differential equations , 2011 .

[20]  Giuseppe Catania,et al.  Analytical Modelling and Experimental Identification of Viscoelastic Mechanical Systems , 2007 .

[21]  Allaberen Ashyralyev,et al.  A note on the fractional Schrödinger differential equations , 2011, Kybernetes.

[22]  F. Mainardi,et al.  Fractals and fractional calculus in continuum mechanics , 1997 .

[23]  N. Ford,et al.  Analysis of Fractional Differential Equations , 2002 .

[24]  V. Lakshmikantham,et al.  Basic theory of fractional differential equations , 2008 .

[25]  Shih-Tong Tu,et al.  Applications of fractional calculus to ordinary and partial differential equations of the second order , 1993 .

[26]  On a non-local boundary problem for a parabolic–hyperbolic equation involving a Riemann–Liouville fractional differential operator , 2012 .

[27]  Ravi P. Agarwal,et al.  Boundary Value Problems for Fractional Differential Equations , 2009 .

[28]  Allaberen Ashyralyev,et al.  A note on fractional derivatives and fractional powers of operators , 2009 .

[29]  Ravi P. Agarwal,et al.  On Type of Periodicity and Ergodicity to a Class of Fractional Order Differential Equations , 2010 .

[30]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[31]  I. Podlubny.  Fractional differential equations , 1998 .

[32]  Thomas J. Osler,et al.  Fractional Derivatives and Special Functions , 1976 .

[33]  S. Sorrentino,et al.  Fractional derivative linear models for describing the viscoelastic dynamic behaviour of polymeric beams , 2006 .

[34]  Allaberen Ashyralyev,et al.  Well-posedness of the Basset problem in spaces of smooth functions , 2011, Appl. Math. Lett..

[35]  Ravi P. Agarwal,et al.  A Survey on Semilinear Differential Equations and Inclusions Involving Riemann-Liouville Fractional Derivative , 2009 .

[36]  Allaberen Ashyralyev,et al.  A note on the fractional hyperbolic differential and difference equations , 2011, Applied Mathematics and Computation.

[37]  Ralf Metzler,et al.  Boundary value problems for fractional diffusion equations , 2000 .

[38]  R. Bagley,et al.  A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity , 1983 .

[39]  Liu Yan-sheng,et al.  Existence of Solution for a Boundary Value Problem of Fractional Order , 2010 .

[40]  M. De la Sen,et al.  Positivity and Stability of the Solutions of Caputo Fractional Linear Time-Invariant Systems of Any Order with Internal Point Delays , 2011 .