scholarly journals Mathematical Modelling and Prediction of the Effect of Chemotherapy on Cancer Cells

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
Hamidreza Namazi ◽  
Vladimir V. Kulish ◽  
Albert Wong
Keyword(s):  
Palliative Care ◽  
Radiation Therapy ◽  
Targeted Therapy ◽  
Diffusion Equation ◽  
Mathematical Modelling ◽  
Cancer Cells ◽  
Hormonal Therapy ◽  
Treatment Options ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation

Abstract Cancer is a class of diseases characterized by out-of-control cells’ growth which affect DNAs and make them damaged. Many treatment options for cancer exist, with the primary ones including surgery, chemotherapy, radiation therapy, hormonal therapy, targeted therapy and palliative care. Which treatments are used depends on the type, location and grade of the cancer as well as the person’s health and wishes. Chemotherapy is the use of medication (chemicals) to treat disease. More specifically, chemotherapy typically refers to the destruction of cancer cells. Considering the diffusion of drugs in cancer cells and fractality of DNA walks, in this research we worked on modelling and prediction of the effect of chemotherapy on cancer cells using Fractional Diffusion Equation (FDE). The employed methodology is useful not only for analysis of the effect of special drug and cancer considered in this research but can be expanded in case of different drugs and cancers.

scholarly journals Nonexistence of global solutions of fractional diffusion equation with time-space nonlocal source

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Abderrazak Nabti ◽  
Ahmed Alsaedi ◽  
Mokhtar Kirane ◽  
Bashir Ahmad
Keyword(s):  
Diffusion Equation ◽  
Global Solutions ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Laplacian Operator ◽  
Nonlocal Source ◽  
Time Space ◽  
Nonexistence Of Solutions ◽  
Beta 2 ◽  
Fractional Laplacian Operator

Abstract We prove the nonexistence of solutions of the fractional diffusion equation with time-space nonlocal source $$\begin{aligned} u_{t} + (-\Delta )^{\frac{\beta }{2}} u =\bigl(1+ \vert x \vert \bigr)^{ \gamma } \int _{0}^{t} (t-s)^{\alpha -1} \vert u \vert ^{p} \bigl\Vert \nu ^{ \frac{1}{q}}(x) u \bigr\Vert _{q}^{r} \,ds \end{aligned}$$ u t + ( − Δ ) β 2 u = ( 1 + | x | ) γ ∫ 0 t ( t − s ) α − 1 | u | p ∥ ν 1 q ( x ) u ∥ q r d s for $(x,t) \in \mathbb{R}^{N}\times (0,\infty )$ ( x , t ) ∈ R N × ( 0 , ∞ ) with initial data $u(x,0)=u_{0}(x) \in L^{1}_{\mathrm{loc}}(\mathbb{R}^{N})$ u ( x , 0 ) = u 0 ( x ) ∈ L loc 1 ( R N ) , where $p,q,r>1$ p , q , r > 1 , $q(p+r)>q+r$ q ( p + r ) > q + r , $0<\gamma \leq 2 $ 0 < γ ≤ 2 , $0<\alpha <1$ 0 < α < 1 , $0<\beta \leq 2$ 0 < β ≤ 2 , $(-\Delta )^{\frac{\beta }{2}}$ ( − Δ ) β 2 stands for the fractional Laplacian operator of order β, the weight function $\nu (x)$ ν ( x ) is positive and singular at the origin, and $\Vert \cdot \Vert _{q}$ ∥ ⋅ ∥ q is the norm of $L^{q}$ L q space.

scholarly journals Classical solutions for a logarithmic fractional diffusion equation

2014 ◽  
Vol 101 (6) ◽  
pp. 901-924 ◽  
Author(s):  
Arturo de Pablo ◽  
Fernando Quirós ◽  
Ana Rodríguez ◽  
Juan Luis Vázquez
Keyword(s):  
Diffusion Equation ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Classical Solutions
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