Generalized function fractional integration operators in some classes of analytic functions
V. Kiryakova (1988)
Matematički Vesnik
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V. Kiryakova (1988)
Matematički Vesnik
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Hongbin Wang, Chenchen Niu (2024)
Czechoslovak Mathematical Journal
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We introduce a type of -dimensional bilinear fractional Hardy-type operators with rough kernels and prove the boundedness of these operators and their commutators on central Morrey spaces with variable exponents. Furthermore, the similar definitions and results of multilinear fractional Hardy-type operators with rough kernels are obtained.
Bouharket Bendouma, Alberto Cabada, Ahmed Hammoudi (2019)
Archivum Mathematicum
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In this article, we study the existence of solutions to systems of conformable fractional differential equations with periodic boundary value or initial value conditions. where the right member of the system is -carathéodory function. We employ the method of solution-tube and Schauder’s fixed-point theorem.
Celso Martínez, Antonia Redondo, Miguel Sanz (2011)
Studia Mathematica
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We present a new method to study the classical fractional integrals of Weyl. This new approach basically consists in considering these operators in the largest space where they make sense. In particular, we construct a theory of fractional integrals of Weyl by studying these operators in an appropriate Fréchet space. This is a function space which contains the -spaces, and it appears in a natural way if we wish to identify these fractional operators with fractional powers of a suitable...
Amouria Hammou, Samira Hamani, Johnny Henderson (2022)
Archivum Mathematicum
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In this article, we study the existence of solutions in a Banach space of boundary value problems for Caputo-Hadamard fractional differential inclusions of order .
Nassim Guerraiche, Samira Hamani, Johnny Henderson (2016)
Archivum Mathematicum
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We establish sufficient conditions for the existence of solutions of a class of fractional functional differential inclusions involving the Hadamard fractional derivative with order . Both cases of convex and nonconvex valued right hand side are considered.
Dariusz Idczak (2017)
Czechoslovak Mathematical Journal
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We introduce a notion of a function of finite fractional variation and characterize such functions together with their weak -additive fractional derivatives. Next, we use these functions to study differential equations of fractional order, containing a -additive term—we prove existence and uniqueness of a solution as well as derive a Cauchy formula for the solution. We apply these results to impulsive equations, i.e. equations containing the Dirac measures.
M. Magdziarz, A. Weron (2007)
Studia Mathematica
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We introduce a fractional Langevin equation with α-stable noise and show that its solution is the stationary α-stable Ornstein-Uhlenbeck-type process recently studied by Taqqu and Wolpert. We examine the asymptotic dependence structure of via the measure of its codependence r(θ₁,θ₂,t). We prove that is not a long-memory process in the sense of r(θ₁,θ₂,t). However, we find two natural continuous-time analogues of fractional ARIMA time series with long memory in the framework of...
Nemat Nyamoradi (2013)
Annales Polonici Mathematici
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We prove the existence of at least three solutions to the following fractional boundary value problem: ⎧ , a.e. t ∈ [0, T], ⎨ ⎩ u (0) = u (T) = 0, where and are the left and right Riemann-Liouville fractional integrals of order 0 ≤ σ < 1 respectively. The approach is based on a recent three critical points theorem of Ricceri [B. Ricceri, A further refinement of a three critical points theorem, Nonlinear Anal. 74 (2011), 7446-7454].
Ali Akbulut, Amil Hasanov (2016)
Open Mathematics
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In this paper, we study the boundedness of fractional multilinear integral operators with rough kernels [...] TΩ,αA1,A2,…,Ak, which is a generalization of the higher-order commutator of the rough fractional integral on the generalized weighted Morrey spaces Mp,ϕ (w). We find the sufficient conditions on the pair (ϕ1, ϕ2) with w ∈ Ap,q which ensures the boundedness of the operators [...] TΩ,αA1,A2,…,Ak, from [...] Mp,φ1wptoMp,φ2wq for 1 < p < q < ∞. In all cases the conditions...
Vakhtang Kokilashvili, Alexander Meskhi (2012)
Studia Mathematica
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rning the boundedness for fractional maximal and potential operators defined on quasi-metric measure spaces from to (trace inequality), where 1 < p < q < ∞, θ > 0 and μ satisfies the doubling condition in X. The results are new even for Euclidean spaces. For example, from our general results D. Adams-type necessary and sufficient conditions guaranteeing the trace inequality for fractional maximal functions and potentials defined on so-called s-sets in ℝⁿ follow. Trace...
Juan Luis Vázquez (2014)
Journal of the European Mathematical Society
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We establish the existence, uniqueness and main properties of the fundamental solutions for the fractional porous medium equation introduced in [51]. They are self-similar functions of the form with suitable and . As a main application of this construction, we prove that the asymptotic behaviour of general solutions is represented by such special solutions. Very singular solutions are also constructed. Among other interesting qualitative properties of the equation we prove an Aleksandrov...
Hussein A.H. Salem (2008)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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In this paper, we study the existence of integrable solutions for the set-valued differential equation of fractional type , a.e. on (0,1), , αₙ ∈ (0,1), where F(t,·) is lower semicontinuous from ℝ into ℝ and F(·,·) is measurable. The corresponding single-valued problem will be considered first.
Saïd Abbas, Mouffak Benchohra, Nadjet Laledj, Yong Zhou (2020)
Archivum Mathematicum
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This article deals with some results about the existence of solutions and bounded solutions and the attractivity for a class of fractional -difference equations. Some applications are made of Schauder fixed point theorem in Banach spaces and Darbo fixed point theorem in Fréchet spaces. We use some technics associated with the concept of measure of noncompactness and the diagonalization process. Some illustrative examples are given in the last section.
María Guadalupe Morales Macías (2024)
Mathematica Bohemica
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This work is devoted to analyzing the existence of the Cauchy fractional-type problems considering the Riemann-Liouville derivative (in the distributional Denjoy integral sense) of real order . These kinds of equations are a generalization of the measure differential equations. Our results extend A. A. Kilbas, H. M. Srivastava, J. J. Trujillo (2006) and H. Zhou, G. Ye, W. Liu, O. Wang (2015).