A study of nonlinear Langevin equation involving two fractional orders in different intervals

B Ahmad, JJ Nieto, A Alsaedi, M El-Shahed - Nonlinear Analysis: Real …, 2012 - Elsevier
This paper studies a nonlinear Langevin equation involving two fractional orders α∈(0, 1]
and β∈(1, 2] with three-point boundary conditions. The contraction mapping principle and …

A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations

B Ahmad, S Ntouyas - Fractional Calculus and Applied Analysis, 2014 - degruyter.com
This paper is concerned with the existence and uniqueness of solutions for a coupled
system of Hadamard type fractional differential equations and integral boundary conditions …

A coupled system of fractional differential equations with nonlocal integral boundary conditions

SK Ntouyas, M Obaid - Advances in Difference Equations, 2012 - Springer
In this paper, we prove the existence and uniqueness of solutions for a system of fractional
differential equations with Riemann-Liouville integral boundary conditions of different order …

Existence results for a system of coupled hybrid fractional differential equations

B Ahmad, SK Ntouyas, A Alsaedi - The Scientific World Journal, 2014 - Wiley Online Library
This paper studies the existence of solutions for a system of coupled hybrid fractional
differential equations with Dirichlet boundary conditions. We make use of the standard tools …

Controllability for a class of fractional neutral integro-differential equations with unbounded delay

V Vijayakumar, A Selvakumar, R Murugesu - Applied Mathematics and …, 2014 - Elsevier
In this paper, we consider a class of fractional neutral integro-differential equations with
unbounded delay in Banach spaces. This paper deals with the exact controllability for …

Stability of logarithmic type for a Hadamard fractional differential problem

MD Kassim, NE Tatar - Journal of Pseudo-Differential Operators and …, 2020 - Springer
We study the long-time behavior of solutions for a general class of nonlinear fractional
differential equations. These equations involve Hadamard fractional derivatives of different …

Positive solutions of an initial value problem for nonlinear fractional differential equations

D Baleanu, H Mohammadi… - Abstract and Applied …, 2012 - Wiley Online Library
We investigate the existence and multiplicity of positive solutions for the nonlinear fractional
differential equation initial value problem D 0+ α u (t)+ D 0+ β u (t)= f (t, u (t)), u (0)= 0, 0< t< …

Boundary value problem of a nonlinear Langevin equation with two different fractional orders and impulses

G Wang, L Zhang, G Song - Fixed Point Theory and Applications, 2012 - Springer
Boundary value problem of a nonlinear Langevin equation with two different fractional orders
and impulses | Fixed Point Theory and Algorithms for Sciences and Engineering Skip to main …

Convergence of solutions of fractional differential equations to power-type functions

MD Kassim, NE Tatar - arXiv preprint arXiv:2011.09562, 2020 - arxiv.org
In this article we study the asymptotic behavior of solutions of some fractional differential
equations. We prove convergence to power type functions under some assumptions on the …

Asymptotic behavior of solutions of fractional differential equations with Hadamard fractional derivatives

MD Kassim, N Tatar - Fractional Calculus and Applied Analysis, 2021 - degruyter.com
The asymptotic behaviour of solutions in an appropriate space is discussed for a fractional
problem involving Hadamard left-sided fractional derivatives of different orders. Reasonable …