Existence results for systems of conformable fractional differential equations

Bouharket Bendouma; Alberto Cabada; Ahmed Hammoudi

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Displaying similar documents to “Existence results for systems of conformable fractional differential equations”

Initial value problems for fractional functional differential inclusions with Hadamard type derivative

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 $α \in (0, 1]$ . Both cases of convex and nonconvex valued right hand side are considered.

Boundary value problems for Caputo-Hadamard fractional differential inclusions in Banach spaces

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 $r \in (0, 1]$ .

Functions of finite fractional variation and their applications to fractional impulsive equations

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 $σ$ -additive fractional derivatives. Next, we use these functions to study differential equations of fractional order, containing a $σ$ -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.

Left general fractional monotone approximation theory

George A. Anastassiou (2016)

Applicationes Mathematicae

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We introduce left general fractional Caputo style derivatives with respect to an absolutely continuous strictly increasing function g. We give various examples of such fractional derivatives for different g. Let f be a p-times continuously differentiable function on [a,b], and let L be a linear left general fractional differential operator such that L(f) is non-negative over a closed subinterval I of [a,b]. We find a sequence of polynomials Qₙ of degree ≤n such that L(Qₙ) is non-negative...

Suitable domains to define fractional integrals of Weyl via fractional powers of operators

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 $L^{p} (ℝ)$ -spaces, and it appears in a natural way if we wish to identify these fractional operators with fractional powers of a suitable...

Pseudo almost periodicity of fractional integro-differential equations with impulsive effects in Banach spaces

Zhinan Xia (2017)

Czechoslovak Mathematical Journal

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In this paper, for the impulsive fractional integro-differential equations involving Caputo fractional derivative in Banach space, we investigate the existence and uniqueness of a pseudo almost periodic $P C$ -mild solution. The working tools are based on the fixed point theorems, the fractional powers of operators and fractional calculus. Some known results are improved and generalized. Finally, existence and uniqueness of a pseudo almost periodic $P C$ -mild solution of a two-dimensional impulsive...

Fractional Langevin equation with α-stable noise. A link to fractional ARIMA time series

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 $Y_{κ} (t), t \geq 0$ is the stationary α-stable Ornstein-Uhlenbeck-type process recently studied by Taqqu and Wolpert. We examine the asymptotic dependence structure of $Y_{κ} (t)$ via the measure of its codependence r(θ₁,θ₂,t). We prove that $Y_{κ} (t)$ 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...

On fractional derivatives

Helena Musielak (1973)

Colloquium Mathematicae

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On a sum of fractional parts

B. Martić (1964)

Matematički Vesnik

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Note on the fractional parts of λθⁿ

Masayoshi Hata (2005)

Acta Arithmetica

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Generalized $H_{m, m}^{m, 0}$ function fractional integration operators in some classes of analytic functions

V. Kiryakova (1988)

Matematički Vesnik

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Existence of solutions of generalized fractional differential equation with nonlocal initial condition

Sandeep P. Bhairat, Dnyanoba-Bhaurao Dhaigude (2019)

Mathematica Bohemica

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This paper is devoted to studying the existence of solutions of a nonlocal initial value problem involving generalized Katugampola fractional derivative. By using fixed point theorems, the results are obtained in weighted space of continuous functions. Illustrative examples are also given.

Mild solution of fractional order differential equations with not instantaneous impulses

Pei-Luan Li, Chang-Jin Xu (2015)

Open Mathematics

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In this paper, we investigate the boundary value problems of fractional order differential equations with not instantaneous impulse. By some fixed-point theorems, the existence results of mild solution are established. At last, one example is also given to illustrate the results.

Multiplicity results for a class of fractional boundary value problems

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: ⎧ $- d / d t (1 / 2_{0} D_{t}^{- σ} (u^{'} (t)) + 1 / 2_{t} D_{T}^{- σ} (u^{'} (t))) - λ β (t) f (u (t)) - μ γ (t) g (u (t)) = 0$ , a.e. t ∈ [0, T], ⎨ ⎩ u (0) = u (T) = 0, where $_{0} D_{t}^{- σ}$ and $_{t} D_{T}^{- σ}$ 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].