Arbitrary order fractional differential equations and inclusions with new integro-multipoint boundary conditions

In this paper, we study a new boundary value problem of arbitrary order fractional differential equations equipped with new integro-multipoint boundary conditions. Existence and uniqueness results for the given problem are obtained by applying the standard tools of fixed point theory. We also extend the problem at hand to its inclusions case and prove an existence result for it by applying a fixed point theorem due to Bohnenblust and Karlin.

[1]  Bashir Ahmad,et al.  SUCCESSIVE ITERATIONS FOR POSITIVE EXTREMAL SOLUTIONS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS ON A HALF-LINE , 2014, Bulletin of the Australian Mathematical Society.

[2]  Shouchuan Hu,et al.  Handbook of multivalued analysis , 1997 .

[3]  Johnny Henderson,et al.  Eigenvalue comparison for fractional boundary value problems with the Caputo derivative , 2014 .

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

[5]  Carla M. A. Pinto,et al.  A delay fractional order model for the co-infection of malaria and HIV/AIDS , 2017 .

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

[7]  Guoping He,et al.  On the uniqueness of solutions for a class of fractional differential equations , 2017, Appl. Math. Lett..

[8]  Ivo Petráš,et al.  Simulation of Drug Uptake in a Two Compartmental Fractional Model for a Biological System. , 2011, Communications in nonlinear science & numerical simulation.

[9]  H. F. Bohnenblust,et al.  On a Theorem of Ville , 1949 .

[10]  J. A. Tenreiro Machado,et al.  A NEW FRACTIONAL DERIVATIVE WITHOUT SINGULAR KERNEL Application to the Modelling of the Steady Heat Flow , 2015, 1601.01623.

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

[12]  Bashir Ahmad,et al.  Dynamic analysis of time fractional order phytoplankton–toxic phytoplankton–zooplankton system , 2015 .

[13]  Donal O’Regan,et al.  Fractional boundary value problems with singularities in space variables , 2013 .

[14]  Zhenlai Han,et al.  Positive solutions for integral boundary value problem of two-term fractional differential equations , 2018, Boundary Value Problems.

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

[16]  Ravi P. Agarwal,et al.  Nonlocal Hadamard fractional boundary value problem with Hadamard integral and discrete boundary conditions on a half-line , 2018, J. Comput. Appl. Math..

[17]  R. Agarwal,et al.  Existence results for coupled nonlinear fractional differential equations equipped with nonlocal coupled flux and multi-point boundary conditions , 2017 .

[18]  Ahmed Alsaedi,et al.  Analytic approximation of solutions of the forced Duffing equation with integral boundary conditions , 2008 .

[19]  Yong Zhou.  Basic Theory of Fractional Differential Equations , 2014 .

[20]  JinRong Wang,et al.  On recent developments in the theory of boundary value problems for impulsive fractional differential equations , 2012, Comput. Math. Appl..

[21]  Bashir Ahmad,et al.  Existence of solutions for a system of fractional differential equations with coupled nonlocal boundary conditions , 2018 .

[22]  K. Deimling.  Multivalued Differential Equations , 1992 .

[23]  Lingju Kong,et al.  Existence of positive solutions to a higher order singular boundary value problem with fractional q-derivatives , 2013 .

[24]  R. Agarwal,et al.  Existence results for sequential fractional integro-differential equations with nonlocal multi-point and strip conditions , 2016 .

[25]  Sotiris K. Ntouyas,et al.  On the existence of solutions for fractional differential inclusions with sum and integral boundary conditions , 2015, Appl. Math. Comput..

[26]  Shurong Sun,et al.  Multi-point boundary value problems for a class of Riemann-Liouville fractional differential equations , 2014 .

[27]  Ravi P. Agarwal,et al.  Fractional Differential Equations with Nonlocal (Parametric Type) Anti-Periodic Boundary Conditions , 2017 .

[28]  W. M. Whyburn.  Differential equations with general boundary conditions , 1942 .

[29]  Feng Gao,et al.  A new fractional derivative involving the normalized sinc function without singular kernel , 2017, 1701.05590.

[30]  Ravi P. Agarwal,et al.  Iterative techniques for the initial value problem for Caputo fractional differential equations with non-instantaneous impulses , 2018, Appl. Math. Comput..

[31]  K. Deimling.  Fixed Point Theory , 2008 .

[32]  A. Alsaedi,et al.  Existence theorems for semi-linear Caputo fractional differential equations with nonlocal discrete and integral boundary conditions , 2016 .

[33]  Yongsheng Ding,et al.  Optimal Control of a Fractional-Order HIV-Immune System With Memory , 2012, IEEE Transactions on Control Systems Technology.

[34]  Johnny Henderson,et al.  Nonexistence of positive solutions for a system of coupled fractional boundary value problems , 2015 .

[35]  R. Agarwal,et al.  A nonlocal multi-point multi-term fractional boundary value problem with Riemann-Liouville type integral boundary conditions involving two indices , 2013 .

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

[37]  Chengbo Zhai,et al.  Properties of positive solutions to a class of four-point boundary value problem of Caputo fractional differential equations with a parameter , 2014, Commun. Nonlinear Sci. Numer. Simul..

[38]  M. Ezzat,et al.  On fractional thermoelasticity , 2011 .

[39]  Raimondas Čiegis,et al.  Numerical approximation of one model of bacterial self-organization , 2012 .

[40]  Ahmed Alsaedi,et al.  Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities , 2017 .