Existence results for Caputo type fractional differential equations with four-point nonlocal fractional integral boundary conditions

This paper presents some existence and uniqueness results for a boundary value problem of fractional differential equations of order � 2 (1,2] with fourpoint nonlocal fractional integral boundary conditions. Our results are based on some standard tools of fixed point theory and nonlinear alternative of LeraySchauder type. Some illustrative examples are also discussed.

[1]  H. Kober ON FRACTIONAL INTEGRALS AND DERIVATIVES , 1940 .

[2]  E. Zeidler,et al.  Fixed-point theorems , 1986 .

[3]  O. Marichev,et al.  Fractional Integrals and Derivatives: Theory and Applications , 1993 .

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

[5]  A. Granas,et al.  Fixed Point Theory , 2003 .

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

[7]  H. Srivastava,et al.  THEORY AND APPLICATIONS OF FRACTIONAL DIFFERENTIAL EQUATIONS. NORTH-HOLLAND MATHEMATICS STUDIES , 2006 .

[8]  O. Agrawal,et al.  Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering , 2007 .

[9]  V. Gafiychuk,et al.  Mathematical modeling of time fractional reaction-diffusion systems , 2008 .

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

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

[12]  Juan J. Nieto,et al.  Maximum principles for fractional differential equations derived from Mittag-Leffler functions , 2010, Appl. Math. Lett..

[13]  Dumitru Baleanu,et al.  On the global existence of solutions to a class of fractional differential equations , 2010, Comput. Math. Appl..

[14]  Bashir Ahmad,et al.  Existence of solutions for irregular boundary value problems of nonlinear fractional differential equations , 2010, Appl. Math. Lett..

[15]  Bashir Ahmad,et al.  On four-point nonlocal boundary value problems of nonlinear integro-differential equations of fractional order , 2010, Appl. Math. Comput..

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

[17]  Zhanbing Bai,et al.  On positive solutions of a nonlocal fractional boundary value problem , 2010 .

[18]  Ravi P. Agarwal,et al.  On nonlocal fractional boundary value problems , 2011 .

[19]  D. O’Regan,et al.  A Nagumo-like uniqueness theorem for fractional differential equations , 2011 .

[20]  Bashir Ahmad,et al.  A FOUR-POINT NONLOCAL INTEGRAL BOUNDARY VALUE PROBLEM FOR FRACTIONAL DIFFERENTIAL EQUATIONS OF ARBITRARY ORDER , 2011 .

[21]  Neville J. Ford,et al.  Fractional boundary value problems: Analysis and numerical methods , 2011 .

[22]  J. Trujillo,et al.  On the existence of solutions of fractional integro-differential equations , 2011 .

[23]  Bashir Ahmad,et al.  Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions , 2011 .

[24]  B. Ahmad,et al.  Anti-periodic fractional boundary value problems with nonlinear term depending on lower order derivative , 2012 .

[25]  K. Diethelm,et al.  Fractional Calculus: Models and Numerical Methods , 2012 .

[26]  B. Ahmad,et al.  A Note on Fractional Differential Equations with Fractional Separated Boundary Conditions , 2012 .