Existence results for a class of generalized fractional boundary value problems

In this paper, we study a class of generalized fractional order three-point boundary value problems that involve fractional derivative defined in terms of weight and scale functions. Using several fixed point theorems, the existence and uniqueness results are obtained.

[1]  K. Deimling Nonlinear functional analysis , 1985 .

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

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

[4]  N. Laskin,et al.  Fractional quantum mechanics , 2008, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  Y. Povstenko FRACTIONAL HEAT CONDUCTION EQUATION AND ASSOCIATED THERMAL STRESS , 2004 .

[6]  M. Zima Fixed point theorem of Leggett–Williams type and its application , 2004 .

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

[8]  R. Gorenflo,et al.  Some recent advances in theory and simulation of fractional diffusion processes , 2007, 0801.0146.

[9]  Tingting Qiu,et al.  Positive solutions for boundary value problem of nonlinear fractional differential equation. , 2008 .

[10]  V. Lakshmikantham,et al.  Theory of Fractional Dynamic Systems , 2009 .

[11]  M. Benchohra,et al.  Boundary value problems for differential equations with fractional order and nonlocal conditions , 2009 .

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

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

[14]  Zhanbing Bai,et al.  Existence results for the three-point impulsive boundary value problem involving fractional differential equations , 2010, Comput. Math. Appl..

[15]  Ravi P. Agarwal,et al.  Existence theory for anti-periodic boundary value problems of fractional differential equations and inclusions , 2011, Comput. Math. Appl..

[16]  A. Cabada,et al.  Positive solutions of nonlinear fractional differential equations with integral boundary value conditions , 2012 .

[17]  O. Agrawal Some generalized fractional calculus operators and their applications in integral equations , 2012 .

[18]  JinRong Wang,et al.  On a new class of impulsive fractional differential equations , 2014, Appl. Math. Comput..

[19]  Yufeng Xu Fractional Boundary Value Problems with Integral and Anti-periodic Boundary Conditions , 2016 .

[20]  Kemei Zhang On a sign-changing solution for some fractional differential equations , 2017 .

[21]  Shuqin Zhang,et al.  Positive solutions to boundary value problems of p-Laplacian with fractional derivative , 2017 .

[22]  Yanyou Qiao,et al.  Existence of solutions for a class of fractional differential equations with integral and anti-periodic boundary conditions , 2017 .