Numerical Solution for Fuzzy Time-Fractional Cancer Tumor Model with a Time-Dependent Net Killing Rate of Cancer Cells

Zureigat, Hamzeh; Al‐Smadi, Mohammed; Al-Khateeb, Areen; Al‐Omari, Shrideh; Alhazmi, Sharifah E.

doi:10.3390/ijerph20043766

Cited by 8 publications

(3 citation statements)

References 40 publications

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“…Fractional differential equations (FDEs) have garnered significant interest due to their wide range of real-life applications in chemistry, physics, biology, engineering, and other fields [1][2][3][4][5][6][7][8][9][10][11][12][13]. In conventional studies on natural processes modeled by FDEs, the vague parameters are considered to be precise and well defined.…”

Section: Introductionmentioning

confidence: 99%

Efficient Numerical Solutions for Fuzzy Time Fractional Convection Diffusion Equations Using Two Explicit Finite Difference Methods

Al-Khateeb

2024

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In this study, we explore fractional partial differential equations as a more generalized version of classical partial differential equations. These fractional equations have shown promise in providing improved descriptions of certain phenomena under specific circumstances. The main focus of this paper comprises the development, analysis, and application of two explicit finite difference schemes to solve an initial boundary value problem involving a fuzzy time fractional convection–diffusion equation with a fractional order in the range of 0≤ ξ ≤ 1. The uniqueness of this problem lies in its consideration of fuzziness within both the initial and boundary conditions. To handle the uncertainty, we propose a computational mechanism based on the double parametric form of fuzzy numbers, effectively converting the problem from an uncertain format to a crisp one. To assess the stability of our proposed schemes, we employ the von Neumann method and find that they demonstrate unconditional stability. To illustrate the feasibility and practicality of our approach, we apply the developed scheme to a specific example.

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Section: Introductionmentioning

confidence: 99%

Efficient Numerical Solutions for Fuzzy Time Fractional Convection Diffusion Equations Using Two Explicit Finite Difference Methods

Al-Khateeb

2024

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“…The surge in attention towards fractional partial differential equations (FPDEs) over recent decades reflects a growing recognition of their versatile applicability across various domains of physics and engineering [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Among the rich tapestry of FPDEs, one stands out prominently: the time fractional diffusion equation.…”

Section: Introductionmentioning

confidence: 99%

Efficient Numerical Solutions for Fuzzy Time Fractional Diffusion Equations Using Two Explicit Compact Finite Difference Methods

Batiha

2024

Computation

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This article introduces an extension of classical fuzzy partial differential equations, known as fuzzy fractional partial differential equations. These equations provide a better explanation for certain phenomena. We focus on solving the fuzzy time diffusion equation with a fractional order of 0 < α ≤ 1, using two explicit compact finite difference schemes that are the compact forward time center space (CFTCS) and compact Saulyev’s scheme. The time fractional derivative uses the Caputo definition. The double-parametric form approach is used to transfer the governing equation from an uncertain to a crisp form. To ensure stability, we apply the von Neumann method to show that CFTCS is conditionally stable, while compact Saulyev’s is unconditionally stable. A numerical example is provided to demonstrate the practicality of our proposed schemes.

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“…Cancer is a condition in which some cells in the body develop uncontrolled and spread to other regions of the body (Zureigat et al, 2023); therefore, blood cancer is a kind of cancer that begins in blood-forming tissue, such as the bone marrow or the cells of the immune system and may be lead to damage. Examples of blood cancer are leukemia, lymphoma, and multiple myeloma.…”

Section: Introductionmentioning

confidence: 99%

Emerging Role of Folate-Mediated One Carbon Metabolism in Leukemia: A Review

Thabit,

Almzaiel

2023

Egyptian Academic Journal of Biological Sciences. C, Physiology

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Leukemia is a type of cancer that develops in the bone marrow and blood cells. When the DNA of a cell undergoes one mutation or a series of mutations results in the formation of leukemia cells. These leukemia cells, "blasts," cannot mature into fully functioning WBCs. Leukemia increases WBCs which compete for space with RBCs and platelets that the body requires to function normally; each may be classified as acute or chronic, myeloid or lymphoid, depending on the originating cell and the growth rate. Nearly 2.5% of all new cancer cases and 3.1% of cancer-related deaths were attributable to Leukemia. Leukemia can strike at any age geographical and ethnic differences in leukemia rates are also present.Folate's significance in cancer was exclusively tied to antifolate-based cancer treatment. After discovering Antifolate associated based chemotherapy, contrary to the inhibitory action of antifolate on tumors, epidemiologic, clinical, and experimental data show that folate deficiency in normal tissues may predispose them to neoplastic transformation and that folate supplementation may suppress the development of tumors in normal tissues. Epidemiologic research reveals a negative connection between folate levels and numerous cancers, including Leukemia. The exact association between folate status and certain cancers is unknown. Vitamin B control one-carbon metabolism and human health. Folatemediated one carbon (1C) metabolism supports a of processes that are essential for the cell. Through a number of interlinked reactions happening in the cytosol and mitochondria of the cell, folate metabolism contributes to de novo purine and thymidylate synthesis, to the methionine cycle and redox defense. Targeting the folate metabolism gave rise to modern chemotherapy. The folate and methionine cycles complete the one-carbon route with vitamin B9 or folate. Vitamin B6 regulates carbon cycling. Vitamin B dysregulation alters biochemical signaling and causes several illnesses.

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Numerical Solution for Fuzzy Time-Fractional Cancer Tumor Model with a Time-Dependent Net Killing Rate of Cancer Cells

Cited by 8 publications

References 40 publications

Efficient Numerical Solutions for Fuzzy Time Fractional Convection Diffusion Equations Using Two Explicit Finite Difference Methods

Efficient Numerical Solutions for Fuzzy Time Fractional Convection Diffusion Equations Using Two Explicit Finite Difference Methods

Efficient Numerical Solutions for Fuzzy Time Fractional Diffusion Equations Using Two Explicit Compact Finite Difference Methods

Emerging Role of Folate-Mediated One Carbon Metabolism in Leukemia: A Review

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