On fractional derivatives
Helena Musielak (1973)
Colloquium Mathematicae
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Displaying similar documents to “Bifurcations of the time-fractional generalized coupled Hirota-Satsuma KdV system”
On fractional derivatives
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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From Newton's equation to fractional diffusion and wave equations.
Vázquez, Luis (2011)
Advances in Difference Equations [electronic only]
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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...
On contraction principle applied to nonlinear fractional differential equations with derivatives of order α ∈ (0,1)
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.
Modelling of Piezothermoelastic Beam with Fractional Order Derivative
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...
A Note On Fractional Integration
Branislav Martić (1973)
Publications de l'Institut Mathématique
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Abstract differential equations of arbitrary (fractional) orders
El-Sayed, Ahmed M. A.
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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.
Hybrid fractional integro-differential inclusions
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.
On a partial Hadamard fractional integral inclusion
Aurelian Cernea (2016)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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We study a class of nonconvex Hadamard fractional integral inclusions and we establish some Filippov type existence results.