Results 161 to 170 of about 1,104,545 (205)

Results on controllability of Hilfer fractional differential equations with infinite delay via measures of noncompactness

Asian journal of control, 2021
This manuscript mainly focuses on the controllability of Hilfer fractional differential system with infinite delay. We study our primary outcomes by employing fractional calculus, measures of noncompactness, and fixed‐point approach.
K. Kavitha, V. Vijayakumar, R. Udhayakumar, C. Ravichandran   +3 more
semanticscholar   +1 more source

Impulsive Caputo-Fabrizio fractional differential equations in b-metric spaces

, 2021
We deal with some impulsive Caputo-Fabrizio fractional differential equations in b b -metric spaces. We make use of α - ϕ \alpha \text{-}\phi -Geraghty-type contraction. An illustrative example is the subject of the last section.
J. Lazreg, S. Abbas, M. Benchohra, E. Karapınar   +3 more
semanticscholar   +1 more source

On solutions of fractional differential equations

AIP Conference Proceedings, 2018
In this paper, we obtain exact and approximate solutions of differential equations by reproducing kernel Hilbert space method. We demonstrate our solutions by series.
Akgul, A., Sakar, M. Giyas
openaire   +3 more sources

Basic Theory of Fractional Differential Equations

, 2014
Fractional Functional Differential Equations Fractional Abstract Differential Equations Fractional Evolution Equations Fractional Boundary Value Problems Fractional Schrodinger Equations Fractional Euler - Lagrange Equations Time-Fractional Diffusion ...
Yong Zhou
semanticscholar   +1 more source

Measure of Noncompactness and Fractional Differential Equations in Frechet Spaces

Dynamic systems and applications, 2020
In this paper, the existence of solutions for an initial value problem of a fractional differential equation is obtained by means of Monch's fixed point theorem and the technique of measures of noncompactness. AMS (MOS) Subject Classification.
Fatima Mesri, M. Benchohra, J. Henderson
semanticscholar   +1 more source

On the fractional differential equations

Applied Mathematics and Computation, 1992
In this paper we are concerned with the semilinear differential equation d^@ax(t)dt^@a=f(t,x(t)), t>;0 where @a is any positive real number. In [3] the author has proved the existence, uniqueness, and some properties of the solution of this equation when ...
openaire   +2 more sources

Mixed Collocation for Fractional Differential Equations

Numerical Algorithms, 2003
We present the mixed collocation method for numerical integration of fractional differential equations of the type D β u=Φ(u,t). Given a regular mesh with constant discretization step, the unknown u(t) is considered as continuous and affine in each cell, and the dynamics Φ(u,t) as a constant.
Dubois, François, Mengué, Stéphanie
openaire   +5 more sources

Fractional Differential Equations

2018
Let the fractional differential equation (FDE) be $$\displaystyle (D^\alpha _{a_+}y)(t) = f[t,y(t)],\hspace {0.2 cm} \alpha > 0,\hspace {0.2 cm} t > a,$$ with the conditions: $$\displaystyle (D^{\alpha - k}_{a+}y)(a+) = b_k,\hspace {0.2 cm} k = 1,\ldots , n,$$ called also Riemann–Liouville FDE.
Constantin Milici, Gheorghe Drăgănescu, J. A. Tenreiro Machado   +2 more
openaire   +2 more sources

Fractional differential equations and the Schrödinger equation

Applied Mathematics and Computation, 2005
In a previous paper, we defined, following a previous work of Kolvankar and Gangal, a notion of @a-derivative ...
Faycal Ben Adda, Jacky Cresson
openaire   +2 more sources

Fractional Differential Equations in Electrochemistry

Civil-Comp Proceedings, 2009
Electrochemistry was one of the first sciences to benefit from the fractional calculus. Electrodes may be thought of as ''transducers'' of chemical fluxes into electricity. In a typical electrochemical cell, chemical species, such as ions or dissolved molecules, move towards the electrodes by diffusion.
openaire   +2 more sources