Fractional order calculus: basic concepts and engineering applications.
Gutiérrez, Ricardo Enrique, Rosário, João Maurício, Machado, José Tenreiro (2010)
Mathematical Problems in Engineering
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Displaying similar documents to “Time-delay and fractional derivatives.”
Fractional order calculus: basic concepts and engineering applications.
An effective numerical method and its utilization to solution of fractional models used in bioengineering applications.
Petráš, Ivo (2011)
Advances in Difference Equations [electronic only]
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Exact solution of impulse response to a class of fractional oscillators and its stability.
Li, Ming, Lim, S.C., Chen, Shengyong (2011)
Mathematical Problems in Engineering
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From Newton's equation to fractional diffusion and wave equations.
Vázquez, Luis (2011)
Advances in Difference Equations [electronic only]
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Design of Fractional Order Digital Differentiators and Integrators Using Indirect Discretization
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...
On fractional derivatives
Helena Musielak (1973)
Colloquium Mathematicae
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The foam drainage equation with time and space-fractional derivatives solved by the adomian method.
Dahmani, Z., Mesmoudi, M.M., Bebbouchi, R. (2008)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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A Poster about the Recent History of Fractional Calculus
Machado, Tenreiro, Kiryakova, Virginia, Mainardi, Francesco (2010)
Fractional Calculus and Applied Analysis
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MSC 2010: 26A33, 05C72, 33E12, 34A08, 34K37, 35R11, 60G22 In the last decades fractional calculus became an area of intense re-search and development. The accompanying poster illustrates the major contributions during the period 1966-2010.
A Fractional LC − RC Circuit
Ayoub, N., Alzoubi, F., Khateeb, H., Al-Qadi, M., Hasan (Qaseer), M., Albiss, B., Rousan, A. (2006)
Fractional Calculus and Applied Analysis
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Mathematics Subject Classification: 26A33, 30B10, 33B15, 44A10, 47N70, 94C05 We suggest a fractional differential equation that combines the simple harmonic oscillations of an LC circuit with the discharging of an RC circuit. A series solution is obtained for the suggested fractional differential equation. When the fractional order α = 0, we get the solution for the RC circuit, and when α = 1, we get the solution for the LC circuit. For arbitrary α we get a general solution...
On a sum of fractional parts
B. Martić (1964)
Matematički Vesnik
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IVPs for singular multi-term fractional differential equations with multiple base points and applications
Yuji Liu, Pinghua Yang (2014)
Applicationes Mathematicae
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The purpose of this paper is to study global existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations. By constructing a special Banach space and employing fixed-point theorems, some sufficient conditions are obtained for the global existence and uniqueness of solutions of this kind of equations involving Caputo fractional derivatives and multiple base points. We apply the results to solve the forced logistic model with multi-term...
Note on the fractional parts of λθⁿ
Masayoshi Hata (2005)
Acta Arithmetica
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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.