On a mean value theorem in the class of Herglotz functions and its applications.
Sakhnovich, A.L., Sakhnovich, L.A. (2008)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Sakhnovich, A.L., Sakhnovich, L.A. (2008)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Seybold, H. J., Hilfer, R. (2005)
Fractional Calculus and Applied Analysis
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Mathematics Subject Classification: 33E12, 33FXX PACS (Physics Abstracts Classification Scheme): 02.30.Gp, 02.60.Gf Results of extensive calculations for the generalized Mittag-Leffler function E0.8,0.9(z) are presented in the region −8 ≤ Re z ≤ 5 and −10 ≤ Im z ≤ 10 of the complex plane. This function is related to the eigenfunction of a fractional derivative of order α = 0.8 and type β = 0.5.
Amina Boucenna, Toufik Moussaoui (2014)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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The aim of this paper is to study the existence of solutions to a boundary value problem associated to a nonlinear fractional differential equation where the nonlinear term depends on a fractional derivative of lower order posed on the half-line. An appropriate compactness criterion and suitable Banach spaces are used and so a fixed point theorem is applied to obtain fixed points which are solutions of our problem.
Manjari Upadhyay (1971)
Annales Polonici Mathematici
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Ahmad El-Nabulsi (2011)
Annales UMCS, Mathematica
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In this work, we communicate the topic of complex Lie algebroids based on the extended fractional calculus of variations in the complex plane. The complexified Euler-Lagrange geodesics and Wong's fractional equations are derived. Many interesting consequences are explored.
Ahmad Rami El-Nabulsi (2011)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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In this work, we communicate the topic of complex Lie algebroids based on the extended fractional calculus of variations in the complex plane. The complexified Euler-Lagrange geodesics and Wong’s fractional equations are derived. Many interesting consequences are explored.
Masayoshi Hata (2005)
Acta Arithmetica
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B. Martić (1964)
Matematički Vesnik
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Helena Musielak (1973)
Colloquium Mathematicae
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Rajneesh Kumar, Poonam Sharma (2016)
Curved and Layered Structures
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This paper deals with the study of transverse vibrations in piezothermoelastic beam resonators with fractional order derivative. The fractional order theory of thermoelasticity developed by Sherief et al. [1] has been used to study the problem. The expressions for frequency shift and damping factor are derived for a thermo micro-electromechanical (MEM) and thermo nano-electromechanical (NEM) beam resonators clamped on one side and free on another. The effect of fractional order derivative...
Branislav Martić (1973)
Publications de l'Institut Mathématique
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Marwan Alquran, Kamel Al-Khaled, Mohammed Ali, Omar Abu Arqub (2017)
Waves, Wavelets and Fractals
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The Hirota-Satsuma model with fractional derivative is considered to provide some characteristics of memory embedded into the system. The modified system is analyzed analytically using a new technique called residual power series method. We observe thatwhen the value of memory index (time-fractional order) is close to zero, the solutions bifurcate and produce a wave-like pattern.
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...
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.