A note on the existence of solutions for some boundary value problems of fractional differential inclusions

2012 ◽  
Vol 15 (2) ◽  
Author(s):  
Aurelian Cernea
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Existence Results ◽  
Fractional Differential Inclusions ◽  
Fractional Differential ◽  
Filippov Type

AbstractWe study the existence of solutions for fractional differential inclusions of order q ∈ (1, 2] with families of mixed and closed boundary conditions. We establish Filippov type existence results in the case of nonconvex setvalued maps.

scholarly journals Boundary value problems for Caputo-Hadamard fractional differential inclusions with Integral Conditions

2020 ◽  
Vol 6 (1) ◽  
pp. 62-75
Author(s):  
Ahmed Zahed ◽  
Samira Hamani ◽  
Johnny Henderson
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Fractional Differential Inclusions ◽  
Integral Conditions ◽  
Right Hand ◽  
Fractional Differential

AbstractFor r ∈ (1, 2], the authors establish sufficient conditions for the existence of solutions for a class of boundary value problem for rth order Caputo-Hadamard fractional differential inclusions satisfying nonlinear integral conditions. Both cases of convex and nonconvex valued right hand sides are considered.

scholarly journals A Countable System of Fractional Inclusions with Periodic, Almost, and Antiperiodic Boundary Conditions

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Ahmed Salem ◽  
Aeshah Al-Dosari
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Differential Inclusions ◽  
Existence Results ◽  
Multivalued Mappings ◽  
Countable System ◽  
Fractional Differential Inclusions ◽  
Inclusion Type ◽  
Fractional Differential

This article is dedicated to the existence results of solutions for boundary value problems of inclusion type. We suggest the infinite countable system to fractional differential inclusions written by D α ABC ν i t ∈ Y i t , ν i t i = 1 ∞ . The mappings y i t , ν i t i = 1 ∞ are proposed to be Lipschitz multivalued mappings. The results are explored according to boundary condition σ ν i 0 = γ ν i ρ ,     σ , γ ∈ ℝ . This type of condition is the generalization of periodic, almost, and antiperiodic types.

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 Boundary Value Problems for Hilfer Fractional Differential Inclusions with Nonlocal Integral Boundary Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1905
Author(s):  
Athasit Wongcharoen ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Differential Inclusions ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Fractional Differential ◽  
Nonlocal Integral Boundary Conditions

In this paper, we study boundary value problems for differential inclusions, involving Hilfer fractional derivatives and nonlocal integral boundary conditions. New existence results are obtained by using standard fixed point theorems for multivalued analysis. Examples illustrating our results are also presented.

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