Results 71 to 80 of about 191,994 (333)

Semilinear ordinary differential equation coupled with distributed order fractional differential equation

, 2009
System of semilinear ordinary differential equation and fractional differential equation of distributed order is investigated and solved in a mild and classical sense.
Atanackovic, Teodor M., Oparnica, Ljubica, Pilipovic, Stevan   +2 more
core   +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

Lie symmetry analysis, conservation laws and exact solutions of the seventh-order time fractional Sawada–Kotera–Ito equation

Results in Physics, 2016
In this paper Lie symmetry analysis of the seventh-order time fractional Sawada–Kotera–Ito (FSKI) equation with Riemann–Liouville derivative is performed.
Emrullah Yaşar, Yakup Yıldırım, Chaudry Masood Khalique   +2 more
doaj   +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

Exact solutions of conformable fractional differential equations

Results in Physics, 2021
This article is about to formulate exact solutions of the time fractional Dodd-Bullough-Mikhailov (DBM) equation, Sinh-Gordon equation and Liouville equation by utilizing simplest equation method (SEM) in conformable fractional derivative (CFD) sense ...
Haleh Tajadodi, Zareen A. Khan, Ateeq ur Rehman Irshad, J.F. Gómez-Aguilar, Aziz Khan, Hasib Khan   +5 more
doaj   +1 more source

Neural fractional differential equations

Applied Mathematical Modelling
Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise representation of processes characterised by non-local and memory-dependent behaviours.
C. Coelho, M. Fernanda P. Costa, L.L. Ferrás   +2 more
openaire   +2 more sources

SEPARABLE LOCAL FRACTIONAL DIFFERENTIAL EQUATIONS [PDF]

Fractals, 2016
The concept of local fractional derivative was introduced in order to be able to study the local scaling behavior of functions. However it has turned out to be much more useful. It was found that simple equations involving these operators naturally incorporate the fractal sets into the equations.
openaire   +3 more sources

Chemoresistome mapping in individual breast cancer patients unravels diversity in dynamic transcriptional adaptation

Molecular Oncology, EarlyView.
This study used longitudinal transcriptomics and gene‐pattern classification to uncover patient‐specific mechanisms of chemotherapy resistance in breast cancer. Findings reveal preexisting drug‐tolerant states in primary tumors and diverse gene rewiring patterns across patients, converging on a few dysregulated functional modules. Despite receiving the
Maya Dadiani, Gilgi Friedlander, Gili Perry, Nora Balint‐Lahat, Shlomit Gilad, Dana Morzaev‐Sulzbach, Anjana Shenoy, Noa Bossel Ben‐Moshe, Anya Pavlovsky, Rinat Bernstein‐Molho, Eytan Domany, Iris Barshack, Tamar Geiger, Bella Kaufman, Einav Nili Gal‐Yam   +14 more
wiley   +1 more source

Fractional Fourier Transform and Ulam Stability of Fractional Differential Equation with Fractional Caputo-Type Derivative

Journal of Function Spaces, 2022
In this paper, we study the Ulam-Hyers-Mittag-Leffler stability for a linear fractional order differential equation with a fractional Caputo-type derivative using the fractional Fourier transform.
Arunachalam Selvam, Sriramulu Sabarinathan, Samad Noeiaghdam, Vediyappan Govindan   +3 more
doaj   +1 more source

Circulating tumor DNA monitoring and blood tumor mutational burden in patients with metastatic solid tumors treated with atezolizumab

Molecular Oncology, EarlyView.
In patients treated with atezolizumab as a part of the MyPathway (NCT02091141) trial, pre‐treatment ctDNA tumor fraction at high levels was associated with poor outcomes (radiographic response, progression‐free survival, and overall survival) but better sensitivity for blood tumor mutational burden (bTMB).
Charles Swanton, Russell W. Madison, Candice Francheska B. Tambaoan, Funda Meric‐Bernstam, Christopher J. Sweeney, Razelle Kurzrock, Howard A. Burris III, David R. Spigel, Hanna Tukachinsky, Jason Hughes, Julia Malato, Bongin Yoo, Tania Szado, Cheryl Schwab, Lincoln W. Pasquina, Amaya Gasco, Katja Schulze, Claire F. Friedman   +17 more
wiley   +1 more source