scholarly journals Impulsive partial hyperbolic differential inclusions of fractional order

2010 ◽  
Vol 43 (4) ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra
Keyword(s):  
Fixed Point ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Caputo Fractional Derivative ◽  
Differential Inclusions ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Hyperbolic Differential Inclusions

AbstractIn this paper we investigate the existence of solutions of a class of partial impulsive hyperbolic differential inclusions involving the Caputo fractional derivative. Our main tools are appropriate fixed point theorems from multivalued analysis.

scholarly journals Existence of Solutions for Anti-Periodic Fractional Differential Inclusions Involving ψ-Riesz-Caputo Fractional Derivative

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 630
Author(s):  
Dandan Yang ◽  
Chuanzhi Bai
Keyword(s):  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Fractional Differential Inclusions ◽  
Nonlinear Alternative ◽  
Contractive Map ◽  
Fractional Differential ◽  
Definition Of

In this paper, we investigate the existence of solutions for a class of anti-periodic fractional differential inclusions with ψ -Riesz-Caputo fractional derivative. A new definition of ψ -Riesz-Caputo fractional derivative of order α is proposed. By means of Contractive map theorem and nonlinear alternative for Kakutani maps, sufficient conditions for the existence of solutions to the fractional differential inclusions are given. We present two examples to illustrate our main results.

scholarly journals Fractional order differential inclusions on an unbounded domain with infinite delay

Mathematica ◽  
2020 ◽  
Vol 62 (85) (2) ◽  
pp. 167-178
Author(s):  
Mohamed Helal
Keyword(s):  
Fractional Order ◽  
Initial Value Problems ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Fréchet Spaces ◽  
Initial Value ◽  
Nonlinear Alternative ◽  
Hyperbolic Differential Inclusions

We provide sufficient conditions for the existence of solutions to initial value problems, for partial hyperbolic differential inclusions of fractional order involving Caputo fractional derivative with infinite delay by applying the nonlinear alternative of Frigon type for multivalued admissible contraction in Frechet spaces.

scholarly journals On Neutral Functional Differential Inclusions involving Hadamard Fractional Derivatives

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1084 ◽  
Author(s):  
Bashir Ahmad ◽  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas ◽  
Hamed H. Al-Sulami
Keyword(s):  
Fixed Point ◽  
Differential Inclusions ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Multivalued Maps ◽  
Functional Differential ◽  
Functional Differential Inclusions

We prove the existence of solutions for neutral functional differential inclusions involving Hadamard fractional derivatives by applying several fixed point theorems for multivalued maps. We also construct examples for illustrating the obtained results.

scholarly journals On Fractional Order Hybrid Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Mohamed A. E. Herzallah ◽  
Dumitru Baleanu
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Fixed Point Theorems ◽  
Mild Solutions ◽  
Nonlinear Perturbations ◽  
Linear And Nonlinear ◽  
Hybrid Differential Equations ◽  
Hybrid Equations

We develop the theory of fractional hybrid differential equations with linear and nonlinear perturbations involving the Caputo fractional derivative of order0<α<1. Using some fixed point theorems we prove the existence of mild solutions for two types of hybrid equations. Examples are given to illustrate the obtained results.

Existence of solutions for Riemann–Liouville multi-valued fractional boundary value problems

2017 ◽  
Vol 24 (4) ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Differential Inclusions ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Fractional Differential Inclusions ◽  
Fractional Differential ◽  
Fractional Boundary Conditions ◽  
Fractional Boundary Value Problems

AbstractIn this paper, we study a class of Riemann–Liouville fractional differential inclusions with fractional boundary conditions. By using standard fixed point theorems, we obtain some new existence results for convex as well as nonconvex multi-valued mappings in an appropriate Banach space. The obtained results are illustrated by examples.

scholarly journals Existence of Solutions for Anti-Periodic Fractional Differential Inclusions with ψ-Caupto Fractional Derivative

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Dandan Yang ◽  
Chuanzhi Bai
Keyword(s):  
Fractional Derivative ◽  
Differential Inclusions ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Fractional Differential Inclusions ◽  
Fractional Differential ◽  
Special Case ◽  
Fractional Boundary Value Problems

In this paper, we investigate the existence of solutions for a class of fractional boundary value problems with anti-periodic boundary value conditions with ψ-Caupto fractional derivative. By means of some standard fixed point theorems, sufficient conditions for the existence of solutions for the fractional differential inclusions with ψ-Caputo derivatives are presented. Our result generalizes the known special case if ψx=x and single known results to the multi-valued ones.

scholarly journals Nonlinear Caputo Fractional Derivative with Nonlocal Riemann-Liouville Fractional Integral Condition Via Fixed Point Theorems

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 829 ◽  
Author(s):  
Piyachat Borisut ◽  
Poom Kumam ◽  
Idris Ahmed ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Integral Condition ◽  
Supremum Norm ◽  
Caputo Fractional Derivatives ◽  
Integral Boundary

In this paper, we study and investigate an interesting Caputo fractional derivative and Riemann–Liouville integral boundary value problem (BVP): c D 0 + q u ( t ) = f ( t , u ( t ) ) , t ∈ [ 0 , T ] , u ( k ) ( 0 ) = ξ k , u ( T ) = ∑ i = 1 m β i R L I 0 + p i u ( η i ) , where n - 1 < q < n , n ≥ 2 , m , n ∈ N , ξ k , β i ∈ R , k = 0 , 1 , ⋯ , n - 2 , i = 1 , 2 , ⋯ , m , and c D 0 + q is the Caputo fractional derivatives, f : [ 0 , T ] × C ( [ 0 , T ] , E ) → E , where E is the Banach space. The space E is chosen as an arbitrary Banach space; it can also be R (with the absolute value) or C ( [ 0 , T ] , R ) with the supremum-norm. R L I 0 + p i is the Riemann–Liouville fractional integral of order p i > 0 , η i ∈ ( 0 , T ) , and ∑ i = 1 m β i η i p i + n - 1 Γ ( n ) Γ ( n + p i ) ≠ T n - 1 . Via the fixed point theorems of Krasnoselskii and Darbo, the authors study the existence of solutions to this problem. An example is included to illustrate the applicability of their results.

scholarly journals On a class of differential inclusions in the frame of generalized Hilfer fractional derivative

2022 ◽  
Vol 7 (3) ◽  
pp. 3477-3493
Author(s):  
Adel Lachouri ◽  
◽  
Mohammed S. Abdo ◽  
Abdelouaheb Ardjouni ◽  
Bahaaeldin Abdalla ◽  
...  
Keyword(s):  
Fixed Point ◽  
Fractional Derivative ◽  
Differential Inclusions ◽  
Fixed Point Theorems ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Hilfer Fractional Derivative ◽  
Integral Boundary ◽  
Inclusion Problems ◽  
Nonlocal Integral Boundary Conditions

<abstract><p>In the present paper, we extend and develop a qualitative analysis for a class of nonlinear fractional inclusion problems subjected to nonlocal integral boundary conditions (nonlocal IBC) under the $ \varphi $-Hilfer operator. Both claims of convex valued and nonconvex valued right-hand sides are investigated. The obtained existence results of the proposed problem are new in the frame of a $ \varphi $-Hilfer fractional derivative with nonlocal IBC, which are derived via the fixed point theorems (FPT's) for set-valued analysis. Eventually, we give some illustrative examples for the acquired results.</p></abstract>

scholarly journals New results on Caputo fractional-order neutral differential inclusions without compactness

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Manar A. Alqudah ◽  
C. Ravichandran ◽  
Thabet Abdeljawad ◽  
N. Valliammal
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fractional Order ◽  
Weak Topology ◽  
Differential Inclusions ◽  
Fixed Point Theorems ◽  
Nonlocal Conditions ◽  
Existence Results ◽  
Neutral System

AbstractThis article deals with existence results of Caputo fractional neutral inclusions without compactness in Banach space using weak topology. In fact, for weakly sequentially closed maps we apply fixed point theorems to obtain the existence of the solution. Furthermore, the results are manifested for fractional neutral system held by nonlocal conditions. To justify the application of the reported results an illustration is presented.

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