Existence of solutions to fractional order ordinary and delay differential equations and applications.
Abbas, Syed (2011)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Similarity:
Displaying similar documents to “A Fractional LC − RC Circuit”
Existence of solutions to fractional order ordinary and delay differential equations and applications.
On a sum of fractional parts
B. Martić (1964)
Matematički Vesnik
Similarity:
Note on the fractional parts of λθⁿ
Masayoshi Hata (2005)
Acta Arithmetica
Similarity:
On fractional derivatives
Helena Musielak (1973)
Colloquium Mathematicae
Similarity:
A Note On Fractional Integration
Branislav Martić (1973)
Publications de l'Institut Mathématique
Similarity:
Theorems on some families of fractional differential equations and their applications
Gülçin Bozkurt, Durmuş Albayrak, Neşe Dernek (2019)
Applications of Mathematics
Similarity:
We use the Laplace transform method to solve certain families of fractional order differential equations. Fractional derivatives that appear in these equations are defined in the sense of Caputo fractional derivative or the Riemann-Liouville fractional derivative. We first state and prove our main results regarding the solutions of some families of fractional order differential equations, and then give examples to illustrate these results. In particular, we give the exact solutions for...
From Newton's equation to fractional diffusion and wave equations.
Vázquez, Luis (2011)
Advances in Difference Equations [electronic only]
Similarity:
Existence of solutions of generalized fractional differential equation with nonlocal initial condition
Sandeep P. Bhairat, Dnyanoba-Bhaurao Dhaigude (2019)
Mathematica Bohemica
Similarity:
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.
Modelling of Piezothermoelastic Beam with Fractional Order Derivative
Rajneesh Kumar, Poonam Sharma (2016)
Curved and Layered Structures
Similarity:
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...
Boundary value problems for differential equations with fractional order.
Benchohra, Mouffak, Hamani, Samira, Ntouyas, Sotiris K. (2008)
Surveys in Mathematics and its Applications
Similarity:
A detailed analysis for the fundamental solution of fractional vibration equation
Li-Li Liu, Jun-Sheng Duan (2015)
Open Mathematics
Similarity:
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...
On contraction principle applied to nonlinear fractional differential equations with derivatives of order α ∈ (0,1)
Małgorzata Klimek (2011)
Banach Center Publications
Similarity:
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.