Note on the fractional parts of λθⁿ
Masayoshi Hata (2005)
Acta Arithmetica
Similarity:
Masayoshi Hata (2005)
Acta Arithmetica
Similarity:
B. Martić (1964)
Matematički Vesnik
Similarity:
Helena Musielak (1973)
Colloquium Mathematicae
Similarity:
Branislav Martić (1973)
Publications de l'Institut Mathématique
Similarity:
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.
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...
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.
Yuji Liu, Pinghua Yang (2014)
Applicationes Mathematicae
Similarity:
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...
Vázquez, Luis (2011)
Advances in Difference Equations [electronic only]
Similarity:
Marwan Alquran, Kamel Al-Khaled, Mohammed Ali, Omar Abu Arqub (2017)
Waves, Wavelets and Fractals
Similarity:
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.
Choukri Derbazi, Hadda Hammouche (2021)
Mathematica Bohemica
Similarity:
We study the existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems. Our results are based on Schauder's fixed point theorem and the Banach contraction principle fixed point theorem. Examples are provided to illustrate the main results.
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...
Pei-Luan Li, Chang-Jin Xu (2015)
Open Mathematics
Similarity:
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.