Non-Linear First-Order Differential Boundary Problems with Multipoint and Integral Conditions

Mardanov, Mısır J.; Sharifov, Yagub A.; Gasimov, Yusif S.; Cattani, Carlo

doi:10.3390/fractalfract5010015

Cited by 9 publications

(2 citation statements)

References 23 publications

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“…A fundamental solution is generally not available if the coefficients of the original partial differential equation are not constant. One can use, in this case, a parametrix (Levi function), which is usually available, instead of fundamental solution Green formulae [3,12,13].…”

Section: Introductionmentioning

confidence: 99%

Analysis of Two-Dimensional Heat Transfer Problem Using the Boundary Integral Equation

Kebeba

Haifo

2022

Advances in Mathematical Physics

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In this paper, we examine the problem of two-dimensional heat equations with certain initial and boundary conditions being considered. In a two-dimensional heat transport problem, the boundary integral equation technique was applied. The problem is expressed by an integral equation using the fundamental solution in Green’s identity. In this study, we transform the boundary value problem for the steady-state heat transfer problem into a boundary integral equation and drive the solution of the two-dimensional heat transfer problem using the boundary integral equation for the mixed boundary value problem by using Green’s identity and fundamental solution.

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Section: Introductionmentioning

confidence: 99%

Analysis of Two-Dimensional Heat Transfer Problem Using the Boundary Integral Equation

Kebeba

Haifo

2022

Advances in Mathematical Physics

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“…See also [20] for a similar study on analogous differential systems. Very recently, the results in [21] were devoted to the study of first-order problems with multipoint and integral boundary conditions by applying Banach or Schaefer's fixed point theorem.…”

Section: Introductionmentioning

confidence: 99%

Existence of Solutions to a Class of Nonlinear Arbitrary Order Differential Equations Subject to Integral Boundary Conditions

2021

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We investigate the existence of positive solutions for a class of fractional differential equations of arbitrary order δ>2, subject to boundary conditions that include an integral operator of the fractional type. The consideration of this type of boundary conditions allows us to consider heterogeneity on the dependence specified by the restriction added to the equation as a relevant issue for applications. An existence result is obtained for the sublinear and superlinear case by using the Guo–Krasnosel’skii fixed point theorem through the definition of adequate conical shells that allow us to localize the solution. As additional tools in our procedure, we obtain the explicit expression of Green’s function associated to an auxiliary linear fractional boundary value problem, and we study some of its properties, such as the sign and some useful upper and lower estimates. Finally, an example is given to illustrate the results.

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On Caputo-Hadamard fractional pantograph problem of two different orders with Dirichlet boundary conditions

Rafeeq,

Thabet,

Mohammed

et al. 2024

Alexandria Engineering Journal

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Non-Linear First-Order Differential Boundary Problems with Multipoint and Integral Conditions

Cited by 9 publications

References 23 publications

Analysis of Two-Dimensional Heat Transfer Problem Using the Boundary Integral Equation

Analysis of Two-Dimensional Heat Transfer Problem Using the Boundary Integral Equation

Existence of Solutions to a Class of Nonlinear Arbitrary Order Differential Equations Subject to Integral Boundary Conditions

On Caputo-Hadamard fractional pantograph problem of two different orders with Dirichlet boundary conditions

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