Results 71 to 80 of about 11,783 (202)

Stability of solutions to impulsive Caputo fractional differential equations

Electronic Journal of Differential Equations, 2016
Stability of the solutions to a nonlinear impulsive Caputo fractional differential equation is studied using Lyapunov like functions. The derivative of piecewise continuous Lyapunov functions among the nonlinear impulsive Caputo differential equation ...
Ravi Agarwal, Snezhana Hristova, Donal O'Regan   +2 more
doaj  

A highly accurate numerical method for solving boundary value problem of generalized Bagley‐Torvik equation

Mathematical Methods in the Applied Sciences, EarlyView.
A highly accurate numerical method is given for the solution of boundary value problem of generalized Bagley‐Torvik (BgT) equation with Caputo derivative of order 0<β<2$$ 0<\beta <2 $$ by using the collocation‐shooting method (C‐SM). The collocation solution is constructed in the space Sm+1(1)$$ {S}_{m+1}^{(1)} $$ as piecewise polynomials of degree at ...
Suzan Cival Buranay, Mtema James Chin, Nazim I. Mahmudov   +2 more
wiley   +1 more source

Fractional Boundary Layer Flow: Lie Symmetry Analysis and Numerical Solution

Mathematics
In this paper, we present a fractional version of the Sakiadis flow described by a nonlinear two-point fractional boundary value problem on a semi-infinite interval, in terms of the Caputo derivative.
Alessandra Jannelli, Maria Paola Speciale   +1 more
doaj   +1 more source

Fractional Vector Calculus and Fractional Maxwell's Equations

, 2011
The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. The main approaches to formulate a FVC, which are used in the
Belleguie, Ben Adda, Ben Adda, Ben Adda, Ben Adda, Brandt, Chen, Cottrill-Shepherd, Engheta, Foley, Gelfand, Genchev, Hussain, Hussain, Kazbekov, Kilbas, Kiryakova, Laskin, Mashhoon, Mashhoon, Mashhoon, McBride, Meerschaert, Metzler, Metzler, Miller, Montroll, Naqvi, Naqvi, Nishimoto, Oldham, Pierantozzi, Podlubny, Ross, Rubin, Samko, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Vasily E. Tarasov, West, Zaslavsky, Zaslavsky   +55 more
core   +1 more source

Exponential Stability of Higher Order Fractional Neutral Stochastic Differential Equation Via Integral Contractors

Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6425-6446, April 2025.
ABSTRACT The well‐posedness results for mild solutions to the fractional neutral stochastic differential system with Rosenblatt process with Hurst index Ĥ∈12,1$$ \hat{H}\in \left(\frac{1}{2},1\right) $$ is discussed in this article. To demonstrate the results, the concept of bounded integral contractors is combined with the stochastic result and ...
Dimplekumar N. Chalishajar, Dhanalakshmi Kasinathan, Ramkumar Kasinathan, Ravikumar Kasinathan   +3 more
wiley   +1 more source

On the Solvability of Caputo -Fractional Boundary Value Problem Involving -Laplacian Operator

Abstract and Applied Analysis, 2013
We consider the model of a Caputo -fractional boundary value problem involving -Laplacian operator. By using the Banach contraction mapping principle, we prove that, under some conditions, the suggested model of the Caputo -fractional boundary value ...
Hüseyin Aktuğlu, Mehmet Ali Özarslan
doaj   +1 more source

Fractional Calculus in Wave Propagation Problems [PDF]

, 2012
Fractional calculus, in allowing integrals and derivatives of any positive order (the term "fractional" kept only for historical reasons), can be considered a branch of mathematical physics which mainly deals with integro-differential equations, where ...
Mainardi, Francesco
core  

A survey on fractional variational calculus

, 2018
Main results and techniques of the fractional calculus of variations are surveyed. We consider variational problems containing Caputo derivatives and study them using both indirect and direct methods.
Almeida, Ricardo, Torres, Delfim F. M.
core   +1 more source

Khalouta transform and applications to Caputo-fractional differential equations

Frontiers in Applied Mathematics and Statistics
The paper aims to utilize an integral transform, specifically the Khalouta transform, an abstraction of various integral transforms, to address fractional differential equations using both Riemann-Liouville and Caputo fractional derivative. We discuss some results and the existence of this integral transform.
Nikita Kumawat, Akanksha Shukla, Manvendra Narayan Mishra, Rahul Sharma, Ravi Shanker Dubey   +4 more
openaire   +2 more sources

Equivalences of Nonlinear Higher Order Fractional Differential Equations With Integral Equations

Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6930-6942, April 2025.
ABSTRACT Equivalences of initial value problems (IVPs) of both nonlinear higher order (Riemann–Liouville type) fractional differential equations (FDEs) and Caputo FDEs with the corresponding integral equations are studied in this paper. It is proved that the nonlinearities in the FDEs can be L1$$ {L}^1 $$‐Carathéodory with suitable conditions.
Kunquan Lan
wiley   +1 more source