Boundary value problems for differential equations with fractional order.
Benchohra, Mouffak, Hamani, Samira, Ntouyas, Sotiris K. (2008)
Surveys in Mathematics and its Applications
Similarity:
Benchohra, Mouffak, Hamani, Samira, Ntouyas, Sotiris K. (2008)
Surveys in Mathematics and its Applications
Similarity:
Wang, Xiaojing, Bai, Chuanzhi (2011)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
Similarity:
Anguraj, A., Karthikeyan, P. (2010)
Fractional Calculus and Applied Analysis
Similarity:
MSC 2010: 34A37, 34B15, 26A33, 34C25, 34K37 In this paper we prove the existence of solutions for fractional impulsive differential equations with antiperiodic boundary condition in Banach spaces. The results are obtained by using fractional calculus' techniques and the fixed point theorems.
Benchohra, Mouffak, Slimani, Boualem Attou (2009)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Similarity:
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.
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.
Amina Boucenna, Toufik Moussaoui (2014)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Similarity:
The aim of this paper is to study the existence of solutions to a boundary value problem associated to a nonlinear fractional differential equation where the nonlinear term depends on a fractional derivative of lower order posed on the half-line. An appropriate compactness criterion and suitable Banach spaces are used and so a fixed point theorem is applied to obtain fixed points which are solutions of our problem.
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.
Natthaphong Thongsalee, Sorasak Laoprasittichok, Sotiris K. Ntouyas, Jessada Tariboon (2015)
Open Mathematics
Similarity:
In this paper we study existence and uniqueness of solutions for a system consisting from fractional differential equations of Riemann-Liouville type subject to nonlocal Erdélyi-Kober fractional integral conditions. The existence and uniqueness of solutions is established by Banach’s contraction principle, while the existence of solutions is derived by using Leray-Schauder’s alternative. Examples illustrating our results are also presented.
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...
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.
Xianmin Zhang, Wenbin Ding, Hui Peng, Zuohua Liu, Tong Shu (2016)
Open Mathematics
Similarity:
In this paper, we study a kind of fractional differential system with impulsive effect and find the formula of general solution for the impulsive fractional-order system by analysis of the limit case (as impulse tends to zero). The obtained result shows that the deviation caused by impulses for fractional-order system is undetermined. An example is also provided to illustrate the result.
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.
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.