Results 91 to 100 of about 697,977 (380)

On Solutions of Fractional order Telegraph Partial Differential Equation by Crank-Nicholson Finite Difference Method

Applied Mathematics and Nonlinear Sciences, 2020
The exact solution is calculated for fractional telegraph partial differential equation depend on initial boundary value problem. Stability estimates are obtained for this equation. Crank-Nicholson difference schemes are constructed for this problem. The
Mahmut Modanlı, Ali Akgül
semanticscholar   +1 more source

A large‐scale retrospective study in metastatic breast cancer patients using circulating tumour DNA and machine learning to predict treatment outcome and progression‐free survival

Molecular Oncology, EarlyView.
There is an unmet need in metastatic breast cancer patients to monitor therapy response in real time. In this study, we show how a noninvasive and affordable strategy based on sequencing of plasma samples with longitudinal tracking of tumour fraction paired with a statistical model provides valuable information on treatment response in advance of the ...
Emma J. Beddowes, Mario Ortega Duran, Solon Karapanagiotis, Alistair Martin, Meiling Gao, Riccardo Masina, Ramona Woitek, James Tanner, Fleur Tippin, Justine Kane, Jonathan Lay, Anja Brouwer, Stephen‐John Sammut, Suet‐Feung Chin, Davina Gale, Dana W. Y. Tsui, Sarah‐Jane Dawson, Nitzan Rosenfeld, Maurizio Callari, Oscar M. Rueda, Carlos Caldas   +20 more
wiley   +1 more source

Oscillation of solutions to nonlinear forced fractional differential equations

Electronic Journal of Differential Equations, 2013
In this article, we study the oscillation of solutions to a nonlinear forced fractional differential equation. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative.
Qinghua Feng, Fanwei Meng
doaj  

Fractional differential equations solved by using Mellin transform

, 2014
In this paper, the solution of the multi-order differential equations, by using Mellin Transform, is proposed. It is shown that the problem related to the shift of the real part of the argument of the transformed function, arising when the Mellin ...
Butera, Salvatore, Di Paola, Mario
core   +1 more source

Analysis of a system of fractional differential equations

Journal of Mathematical Analysis and Applications, 2004
The authors investigate the system of fractional differential equations \[ D^\alpha [\overline {x}(t)- \overline {x}(0)]= A\overline {x}(t), \qquad \overline {x}(0)= \overline {x}_0, \quad 0< \alpha< 1, \] where \(D^\alpha\) denotes the Riemannian-Liouville derivative operator and \(A\) is a square matrix having real entries.
Azizollah Babakhani, Varsha Daftardar-Gejji   +1 more
openaire   +2 more sources

Escape from TGF‐β‐induced senescence promotes aggressive hallmarks in epithelial hepatocellular carcinoma cells

Molecular Oncology, EarlyView.
Chronic TGF‐β exposure drives epithelial HCC cells from a senescent state to a TGF‐β resistant mesenchymal phenotype. This transition is characterized by the loss of Smad3‐mediated signaling, escape from senescence, enhanced invasiveness and metastatic potential, and upregulation of key resistance modulators such as MARK1 and GRM8, ultimately promoting
Minenur Kalyoncu, Dilara Demirci, Sude Eris, Bengisu Dayanc, Ece Cakiroglu, Merve Basol, Merve Uysal, Gulcin Cakan‐Akdogan, Fang Liu, Mehmet Ozturk, Gökhan Karakülah, Serif Senturk   +11 more
wiley   +1 more source

Global Existence and Uniqueness of Solution of Atangana–Baleanu Caputo Fractional Differential Equation with Nonlinear Term and Approximate Solutions

International Journal of Differential Equations, 2021
In this paper, a class of fractional order differential equation expressed with Atangana–Baleanu Caputo derivative with nonlinear term is discussed.
Meryeme Hassouna, El Hassan El Kinani, Abdelaziz Ouhadan   +2 more
doaj   +1 more source

A Fractional Lie Group Method For Anomalous Diffusion Equations [PDF]

, 2010
Lie group method provides an efficient tool to solve a differential equation. This paper suggests a fractional partner for fractional partial differential equations using a fractional characteristic method.
Wu, Guo-cheng
core  

Positive Solutions for Boundary Value Problems of Fractional Differential Equation with Integral Boundary Conditions

, 2018
By using two fixed-point theorems on cone, we discuss the existence results of positive solutions for the following boundary value problem of fractional differential equation with integral boundary conditions: , , , and .
Qiao‐Xi Sun, Hong-Kyu Ji, Yujun Cui
semanticscholar   +1 more source

Analytic Solution of Linear Fractional Differential Equation with Jumarie Derivative in Term of Mittag- Leffler Function [PDF]

, 2015
There is no unified method to solve the fractional differential equation. The type of derivative here used in this paper is of Jumarie formulation, for the several differential equations studied.
U. Ghosh, Srijan Sengupta, S. Sarkar, S. Das   +3 more
semanticscholar   +1 more source