Anastassiou, George A., Duman, Oktay (2009)
Serdica Mathematical Journal
Similarity:
2000 Mathematics Subject Classification: 41A25, 41A36, 40G15. In this paper, we obtain some statistical Korovkin-type approximation theorems including fractional derivatives of functions. We also show that our new results are more applicable than the classical ones.
Marvin Barsky (1972)
Annales Polonici Mathematici
Similarity:
Helena Musielak (1973)
Colloquium Mathematicae
Similarity:
Masayoshi Hata (2005)
Acta Arithmetica
Similarity:
B. Martić (1964)
Matematički Vesnik
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.
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.
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...
Sotiris K. Ntouyas, Sorasak Laoprasittichok, Jessada Tariboon (2015)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Similarity:
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.
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...
Aurelian Cernea (2016)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Similarity:
We study a class of nonconvex Hadamard fractional integral inclusions and we establish some Filippov type existence results.
Machado, Tenreiro, Kiryakova, Virginia, Mainardi, Francesco (2010)
Fractional Calculus and Applied Analysis
Similarity:
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.
Tariboon Jessada, Sotiris K. Ntouyas, Suphawat Asawasamrit, Chanon Promsakon (2017)
Open Mathematics
Similarity:
In this paper, we investigate the existence of positive solutions for Hadamard type fractional differential system with coupled nonlocal fractional integral boundary conditions on an infinite domain. Our analysis relies on Guo-Krasnoselskii’s and Leggett-Williams fixed point theorems. The obtained results are well illustrated with the aid of examples.
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...