JinRong Wang, Wei Wei (2012)
Annales Polonici Mathematici
This paper is mainly concerned with existence of mild solutions and optimal controls for nonlinear delay integrodifferential systems with Caputo fractional derivative in infinite-dimensional spaces. We do not assume that the relevant strongly continuous semigroup is compact.
Shcheglova, A.A. (2007)
Sibirskij Matematicheskij Zhurnal
Williams, Lloyd K. (1978)
International Journal of Mathematics and Mathematical Sciences
Yajima, Takahiro, Nagahama, Hiroyuki (2008)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
Djamila Seba (2017)
Mathematica Bohemica
We consider a nonlinear fractional differential inclusion with nonlocal fractional integro-differential boundary conditions in a Banach space. The existence of at least one solution is proved by using the set-valued analog of Mönch fixed point theorem associated with the technique of measures of noncompactness.
Bashir Ahmad, Sotiris K. Ntouyas (2012)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
This article studies a boundary value problem of nonlinear fractional differential inclusions with anti-periodic type integral boundary conditions. Some existence results are obtained via fixed point theorems. The cases of convex-valued and nonconvex-valued right hand sides are considered. Several new results appear as a special case of the results of this paper.
Mouffak Benchohra, Soufyane Bouriah, Jamal E. Lazreg, Juan J. Nieto (2016)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
In this paper, we establish sufficient conditions for the existence of solutions for nonlinear Hadamard-type implicit fractional differential equations with finite delay. The proof of the main results is based on the measure of noncompactness and the Darbo’s and Mönch’s fixed point theorems. An example is included to show the applicability of our results.
Baxley, John V., Enloe, Cynthia G. (2003)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Papalini, Francesca (2007)
Abstract and Applied Analysis
D. Przeworska-Rolewicz (2010)
Annales Polonici Mathematici
We consider nonlinear equations in linear spaces and algebras which can be solved by a "separation of variables" obtained due to Algebraic Analysis. It is shown that the structures of linear spaces and commutative algebras (even if they are Leibniz algebras) are not rich enough for our purposes. Therefore, in order to generalize the method used for separable ordinary differential equations, we have to assume that in algebras under consideration there exist logarithmic mappings. Section 1 contains...
Pagnini, Gianni (2011)
Fractional Calculus and Applied Analysis
MSC 2010: 34A08 (main), 34G20, 80A25The application of Fractional Calculus in combustion science to model the evolution in time of the radius of an isolated premixed flame ball is highlighted. Literature equations for premixed flame ball radius are rederived by a new method that strongly simplifies previous ones. These equations are nonlinear time-fractional differential equations of order 1/2 with a Gaussian underlying diffusion process. Extending the analysis to self-similar anomalous diffusion...
Jeong, Jin-Mun, Jeong, Doo-Hoan, Park, Jong-Yeoul (2000)
International Journal of Mathematics and Mathematical Sciences
Yang, Liu, Chen, Haibo (2011)
Advances in Difference Equations [electronic only]
Boucherif, Abdelkader (2002)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Kwun, Young Chel, Kim, Jeong Soon, Park, Min Ji, Park, Jin Han (2009)
Advances in Difference Equations [electronic only]
Liang, Jin, Fan, Zhenbin (2011)
Advances in Difference Equations [electronic only]
Dimovski, Ivan H., Hristov, Valentin Z. (2009)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Benchohra, Mouffak, Gatsori, Efrosini P., Ntouyas, Sotiris K. (2002)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Martina Pavlačková, Valentina Taddei (2023)
Archivum Mathematicum
We study the existence of a mild solution to the nonlocal initial value problem for semilinear second-order differential inclusions in abstract spaces. The result is obtained by combining the Kakutani fixed point theorem with the approximation solvability method and the weak topology. This combination enables getting the result without any requirements for compactness of the right-hand side or of the cosine family generated by the linear operator.
Chicone, Carmen, Felts, Kenny (2008)
Electronic Journal of Differential Equations (EJDE) [electronic only]