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Fractional Differential Equations, Inclusions and Inequalities with Applications [PDF]

, 2020
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Stochastic fractional differential inclusion driven by fractional Brownian motion

Random Operators and Stochastic Equations, 2023
Abstract In this paper, we prove the existence result for a mild solution of a fractional stochastic evolution inclusion involving the Caputo derivative in the Hilbert space driven by a fractional Brownian motion with the Hurst parameter
Moulay Hachemi, Rahma Yasmina, Guendouzi, Toufik   +1 more
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Fractional integral problems for Hadamard–Caputo fractional Langevin differential inclusions

Journal of Applied Mathematics and Computing, 2015
The authors consider the differential inclusion (of fractional type) \[ D^{\alpha}\big(D^{\beta}+\lambda\big)x(t)\in F\big(t,x(t)\big) \] for \(t\in[1,e]\). The differential inclusion is subjected to the conditions (of nonlocal type) \[ \sum_{i=1}^{m}\theta_{i}I^{\mu_i}x\left(\eta_i\right)=\sum_{j=1}^{n}\phi_{j}I^{\gamma_j}x\left(\omega_j\right) \] and
Ntouyas, Sotiris K., Tariboon, Jessada
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Positive Solutions of Fractional Differential Inclusions at Resonance

Mediterranean Journal of Mathematics, 2013
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Chen, Yi, Tang, Xianhua, He, Xiaofei
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On a Fractional Differential Inclusion with “Maxima”

Fractional Calculus and Applied Analysis, 2016
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Approximate controllability of Riemann–Liouville fractional differential inclusions

Applied Mathematics and Computation, 2016
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Yang, Min, Wang, Qiru
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Stochastic differential inclusions with Hilfer fractional derivative

Annals of the University of Craiova, Mathematics and Computer Science Series, 2022
In this paper, we study the existence of mild solutions of Hilfer fractional stochastic differential inclusions driven by sub fractional Brownian motion in the cases when the multivalued map is convex and non convex. The results are obtained by using fixed point theorem. Finally an example is given to illustrate the obtained results.
Meryem Chaouche, Toufik Guendouzi
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On Fractional Differential Inclusions with Nonlocal Boundary Conditions

Fractional Calculus and Applied Analysis, 2019
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Castaing, Charles, Godet-Thobie, C., Phung, Phan, Truong, Le   +3 more
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On controllability for fractional differential inclusion

2012 IEEE 4th International Conference on Nonlinear Science and Complexity (NSC), 2012
We consider a fractional differential inclusion involving Caputo's fractional derivative and we obtain a sufficient condition for h-local controllability along a reference trajectory. To derive this result we use convex linearizations of the fractional differential inclusion.
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Fractional functional differential inclusions with finite delay

Nonlinear Analysis: Theory, Methods & Applications, 2009
The authors present an existence theorem for solutions of delay differential inclusions of fractional order and discuss some related questions.
Henderson, Johnny, Ouahab, Abdelghani
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