The Choice of the Regularization Parameter for Solving Linear Volterra-Stieltjes Integral Equations of the Third Kind

Bedelova, Nurgul Salibaevna

doi:10.1007/978-3-030-47945-9_36

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2021

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“…Differential and integral equations theory considering fractional order are relevant in mathematics nowadays, which have numerous applications in various fields, physics, mechanics, control theory, engineering, electrochemistry, bioengineering, viscoelasticity, porous media [1] [2] [3]. Solution of the nonlinear integral equation of Volterra-Stieltjes type, and the method is based on an equivalence relation between the fractional differential equation, and Volterra-Stieltjes integral equation of the second kind was also reported in our previous works [4] [5].…”

Section: Introductionmentioning

confidence: 99%

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Regularization and Choice of the Parameter for the Third Kind Nonlinear Volterra-Stieltjes Integral Equation Solutions

Bedelova¹,

Асанов²,

Orozmamatova³

et al. 2021

IJMNTA

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The article is considering the third kind of nonlinear Volterra-Stieltjes integral equations with the solution by Lavrentyev regularizing operator. A uniqueness theorem was proved, and a regularization parameter was chosen. This can be used in further development of the theory of the integral equations in non-standard problems, classes in the numerical solution of third kind Volterra-Stieltjes integral equations, and when solving specific problems that lead to equations of the third kind.

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Section: Introductionmentioning

confidence: 99%

“…Lavrentyev and proved the uniqueness theorem [21] [22]. The regularization parameter is chosen for solving the linear Volterra-Stieltjes integral equation of the third kind [4].…”

Section: Introductionmentioning

confidence: 99%