Some Common Fixed Point Theorems for Generalized F-Contraction Involving w-Distance with Some Applications to Differential Equations

Mongkolkeha, Chirasak; Gopal, Dhananjay

doi:10.3390/math7010032

Cited by 5 publications

(3 citation statements)

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“…Therefore, we fix the parameter values k = 2, f = 1, and s = 10. The value of parameter p is in the range of [10,20]. Thus, p = 20 is the strongest immune system strength, but = 10 is the weakest one.…”

Section: Simulations Using Different Immune Strengthsmentioning

confidence: 99%

“…The applications of mathematical models enable us to study the dynamics and symmetrical property of the immune system as well as to discover the mechanisms controlling tumor cells, to design the therapy schemes, and to predict the outcomes of new therapy strategies [9][10][11][12][13][14][15][16][17][18][19]. In addition, theoretical analysis, modeling methodologies, and symmetrical analysis techniques have been applied to investigate various properties of mathematical models using differential equations [20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

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Mathematical Modeling and Analysis of Tumor Chemotherapy

et al. 2022

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Cancer diseases lead to the second-highest death rate all over the world. For treating tumors, one of the most common schemes is chemotherapy, which can decrease the tumor size and control the progression of cancer diseases. To better understand the mechanisms of chemotherapy, we developed a mathematical model of tumor growth under chemotherapy. This model includes both immune system response and drug therapy. We characterize the symmetrical properties and dynamics of this differential equation model by finding the equilibrium points and exploring the stability and symmetry properties in a range of model parameters. Sensitivity analyses suggest that the chemotherapy drug-induced tumor mortality rate and the drug decay rate contribute significantly to the determination of treatment outcomes. Numerical simulations highlight the importance of CTL activation in tumor chemotherapy.

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Section: Simulations Using Different Immune Strengthsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling and Analysis of Tumor Chemotherapy

et al. 2022

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“…In [22], the authors give the existence results for two-point boundary value problem of fractional differential equations at resonance by means of the coincidence degree theory. Mongkolkeha and Gopal [23] proposed new common fixed-point theorems for the Ciric type generalized Fcontraction in metric spaces with the w-distance. The fixed points for the monotone γ-nonexpansive and generalized ℘ -nonexpansive mappings in hyperbolic space have been approximated by [24].…”

Section: Introductionmentioning

confidence: 99%

Certain Analysis of Solution for the Nonlinear Two-Point Boundary Value Problem with Caputo Fractional Derivative

Murad

2022

Journal of Function Spaces

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In this paper, the existence and uniqueness of solutions for a nonlinear fractional differential equation with a two-point boundary condition in a Banach space are investigated by using the contraction mapping principle and the Brouwer fixed-point theorem with Bielecki norm. The iterative scheme of the numerical solution for the nonlinear two-point boundary value problem will be discussed and illustrated by solving some problems. The well-known Ulam-Hyers and Ulam-Hyers-Rassias stability theorems are employed to establish the stability of solutions to the boundary value problem. In the end, we provided a couple of examples to support our results.

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