Metrical theorems on fractional parts of real sequences.
Glyn Harman (1989)
Journal für die reine und angewandte Mathematik
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Glyn Harman (1989)
Journal für die reine und angewandte Mathematik
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W.J. LeVeque (1959)
Journal für die reine und angewandte Mathematik
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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...
B. Martić (1964)
Matematički Vesnik
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Masayoshi Hata (2005)
Acta Arithmetica
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Branislav Martić (1973)
Publications de l'Institut Mathématique
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Helena Musielak (1973)
Colloquium Mathematicae
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Krishna, B., Reddy, K. (2008)
Fractional Calculus and Applied Analysis
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Mathematics Subject Classification: 26A33, 93B51, 93C95 In this paper, design of fractional order digital differentiators and integrators using indirect discretization is presented. The proposed approach is based on using continued fraction expansion to find the rational approximation of the fractional order operator, s^α. The rational approximation thus obtained is discretized by using s to z transforms. The proposed approach is tested for differentiators and integrators...
Sotiris K. Ntouyas, Sorasak Laoprasittichok, Jessada Tariboon (2015)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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In this paper we study an existence result for initial value problems for hybrid fractional integro-differential inclusions. A hybrid fixed point theorem for a sum of three operators due to Dhage is used. An example illustrating the obtained result is also presented.
Benchohra, Mouffak, Hamani, Samira, Ntouyas, Sotiris K. (2008)
Surveys in Mathematics and its Applications
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Natthaphong Thongsalee, Sorasak Laoprasittichok, Sotiris K. Ntouyas, Jessada Tariboon (2015)
Open Mathematics
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In this paper we study existence and uniqueness of solutions for a system consisting from fractional differential equations of Riemann-Liouville type subject to nonlocal Erdélyi-Kober fractional integral conditions. The existence and uniqueness of solutions is established by Banach’s contraction principle, while the existence of solutions is derived by using Leray-Schauder’s alternative. Examples illustrating our results are also presented.
Małgorzata Klimek (2011)
Banach Center Publications
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One-term and multi-term fractional differential equations with a basic derivative of order α ∈ (0,1) are solved. The existence and uniqueness of the solution is proved by using the fixed point theorem and the equivalent norms designed for a given value of parameters and function space. The explicit form of the solution obeying the set of initial conditions is given.
Li-Li Liu, Jun-Sheng Duan (2015)
Open Mathematics
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In this paper, we investigate the solution of the fractional vibration equation, where the damping term is characterized by means of the Caputo fractional derivative with the order α satisfying 0 < α < 1 or 1 < α < 2. Detailed analysis for the fundamental solution y(t) is carried out through the Laplace transform and its complex inversion integral formula. We conclude that y(t) is ultimately positive, and ultimately decreases monotonically and approaches zero for the case...