Impulsive fractional differential equations in Banach spaces.
Benchohra, M., Seba, D. (2009)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
Similarity:
Displaying similar documents to “Existence of mild solutions for fractional evolution equations with nonlocal initial conditions”
Impulsive fractional differential equations in Banach spaces.
Nonlinear fractional differential inclusion with nonlocal fractional integro-differential boundary conditions in Banach spaces
Djamila Seba (2017)
Mathematica Bohemica
Similarity:
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.
Existence results for impulsive semilinear fractional differential inclusions with delay in Banach spaces
Hammouche Hadda, Guerbati Kaddour, Benchohra Mouffak, Abada Nadjat (2013)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Similarity:
In this paper, we introduce a new concept of mild solution of some class of semilinear fractional differential inclusions of order 0 < α < 1. Also we establish an existence result when the multivalued function has convex values. The result is obtained upon the nonlinear alternative of Leray-Schauder type.
On a nonlocal problem for fractional integrodifferential inclusions in Banach spaces
Zuomao Yan (2011)
Annales Polonici Mathematici
Similarity:
This paper investigates a class of fractional functional integrodifferential inclusions with nonlocal conditions in Banach spaces. The existence of mild solutions of these inclusions is determined under mixed continuity and Carathéodory conditions by using strongly continuous operator semigroups and Bohnenblust-Karlin's fixed point theorem.
Results for Mild solution of fractional coupled hybrid boundary value problems
Dumitru Baleanu, Hossein Jafari, Hasib Khan, Sarah Jane Johnston (2015)
Open Mathematics
Similarity:
The study of coupled system of hybrid fractional differential equations (HFDEs) needs the attention of scientists for the exploration of its different important aspects. Our aim in this paper is to study the existence and uniqueness of mild solution (EUMS) of a coupled system of HFDEs. The novelty of this work is the study of a coupled system of fractional order hybrid boundary value problems (HBVP) with n initial and boundary hybrid conditions. For this purpose, we are utilizing some...
The global existence of mild solutions for semilinear fractional Cauchy problems in the α-norm
Rong-Nian Wang, De-Han Chen, Yan Wang (2012)
Annales Polonici Mathematici
Similarity:
We study the local and global existence of mild solutions to a class of semilinear fractional Cauchy problems in the α-norm assuming that the operator in the linear part is the generator of a compact analytic C₀-semigroup. A suitable notion of mild solution for this class of problems is also introduced. The results obtained are a generalization and continuation of some recent results on this issue.
Mild solution of fractional order differential equations with not instantaneous impulses
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.
Existence and uniqueness of solutions to impulsive fractional differential equations.
Benchohra, Mouffak, Slimani, Boualem Attou (2009)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Similarity:
Boundary value problems for differential equations with fractional order.
Benchohra, Mouffak, Hamani, Samira, Ntouyas, Sotiris K. (2008)
Surveys in Mathematics and its Applications
Similarity:
Existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems
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.
Impulsive Fractional Differential Inclusions Involving the Caputo Fractional Derivative
Ait Dads, E., Benchohra, M., Hamani, S. (2009)
Fractional Calculus and Applied Analysis
Similarity:
Mathematics Subject Classification: 26A33, 34A37. In this paper, we establish sufficient conditions for the existence of solutions for a class of initial value problem for impulsive fractional differential inclusions involving the Caputo fractional derivative. Both cases of convex and nonconvex valued right-hand side are considered. The topological structure of the set of solutions is also considered.
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.
Periodic boundary value problems for nonlinear impulsive fractional differential equation.
Wang, Xiaojing, Bai, Chuanzhi (2011)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
Similarity:
Nonlinear Implicit Hadamard’s Fractional Differential Equationswith Delay in Banach Space
Mouffak Benchohra, Soufyane Bouriah, Jamal E. Lazreg, Juan J. Nieto (2016)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
Similarity:
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.