scholarly journals Existence results for higher order fractional differential inclusions with multi-strip fractional integral boundary conditions

2013 ◽  
pp. 1-19 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris Ntouyas
Keyword(s):  
Boundary Conditions ◽  
Differential Inclusions ◽  
Fractional Integral ◽  
Integral Boundary Conditions ◽  
Higher Order ◽  
Existence Results ◽  
Fractional Differential Inclusions ◽  
Integral Boundary ◽  
Fractional Differential

scholarly journals Existence Results for Fractional Differential Inclusions with Multivalued Term Depending on Lower-Order Derivative

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Xiaoyou Liu ◽  
Zhenhai Liu
Keyword(s):  
Boundary Conditions ◽  
Lower Order ◽  
Differential Inclusions ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Inclusion Problem ◽  
Fractional Differential Inclusions ◽  
Integral Boundary ◽  
Separated Boundary Conditions ◽  
Fractional Differential

This paper is concerned with a class of fractional differential inclusions whose multivalued term depends on lower-order fractional derivative with fractional (non)separated boundary conditions. The cases of convex-valued and non-convex-valued right-hand sides are considered. Some existence results are obtained by using standard fixed point theorems. A possible generalization for the inclusion problem with integral boundary conditions is also discussed. Examples are given to illustrate the results.

scholarly journals Existence Results for Langevin Fractional Differential Inclusions Involving Two Fractional Orders with Four-Point Multiterm Fractional Integral Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas ◽  
Bashir Ahmad
Keyword(s):  
Boundary Conditions ◽  
Differential Inclusions ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Integral Boundary Conditions ◽  
Fractional Differential Inclusions ◽  
Integral Boundary ◽  
Fractional Differential ◽  
The Right ◽  
Fractional Orders

We discuss the existence of solutions for Langevin fractional differential inclusions involving two fractional orders with four-point multiterm fractional integral boundary conditions. Our study relies on standard fixed point theorems for multivalued maps and covers the cases when the right-hand side of the inclusion has convex as well as nonconvex values. Illustrative examples are also presented.

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