On an initial value problem for time fractional pseudo‐parabolic equation with Caputo derivative

Luc, Nguyen Hoang; Jafari, Hossein; Tuan, Nguyen Huy

doi:10.1002/mma.7204

Cited by 10 publications

(8 citation statements)

References 26 publications

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“…Recently, many authors have been involved in the development of fractional analysis. Its applications often appear in areas such as capacitor theory, engineering, electrode-electrolyte interface models feedback amplifers, medical, [2, 5-7, 24, 34], Jafari and his group [15,19,30,32], Inc and his group [3,23,36], and Hammouch and her group [17,20,21]. Due to the application needs of different models, many hierarchical derivative operators arise.…”

Section: Introductionmentioning

confidence: 99%

Well-posed results for nonlocal fractional parabolic equation involving Caputo-Fabrizio operator

Phong¹,

Long²

2022

J. Math. Computer Sci.

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In this paper, we study the parabolic problem associated with non-local conditions, with the Caputo-Fabrizio derivative. Equations on the sphere have many important applications in physics, phenomena, and oceanography. The main motivation for us to study non-local boundary value problems comes from two main reasons: the first reason is that current major interest in several application areas. The second reason is to study approximation for the terminal value problem. With some given data, we prove that the problem has only the solution for two cases. In case = 0, we prove the problem has a local solution. In case > 0, then the problem has a global solution. The main tools and techniques in our demonstration are of using Banach's fixed point theorem in conjunction with some Fourier series analysis involved some evaluation of spherical harmonic function. Several upper and lower upper limit techniques for the Mittag-Lefler functions are also applied.

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Section: Introductionmentioning

confidence: 99%

Well-posed results for nonlocal fractional parabolic equation involving Caputo-Fabrizio operator

Phong¹,

Long²

2022

J. Math. Computer Sci.

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“…Fractional analysis has many applications in mechanics, physics and engineering science, etc. We would like to share many published works on these issues such as E. Karapinar et al [1,2,3,4,5,6,7,8], H. Jafari and his group [18,19,20,21]. When examining mathematical models, depending on the models, there will be many corresponding derivatives.…”

Section: Introductionmentioning

confidence: 99%

Semilinear parabolic diffusion systems on the sphere with Caputo-Fabrizio operator

Binh

2022

Advances in the Theory of Nonlinear Analysis and Its Application

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PDEs on spheres have many important applications in physical phenomena, oceanography and meteorology, geophysics. In this paper, we study the parabolic systems with Caputo-Fabrizio derivative. In order to establish the existence of the mild solution, we use the Banach xed point theorem and some analysis of Fourier series associated with several evaluations of the spherical harmonics function. Some of the techniques on upper and lower bounds of the Mittag-Leer functions are also applied. This is one of the rst research results on the systems of parabolic diusion on the sphere.

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“…Partial differential equations (PDEs) have applications in many branches of science and engineering; see for example [25,20,27,38,29,23,34,11,32]. In this paper, we consider the initial value problem for the conformable heat equation (or called parabolic equation with conformable operator)…”

Section: Introductionmentioning

confidence: 99%

REGULARIZATION FOR TWO INVERSE PROBLEMS FOR CONFORMABLE HEAT EQUATION IN L s SPACES

2022

Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan

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The main goal of the paper is to approximating two types of inverse problems for conformable heat equation (or called parabolic equation with conformable operator). The conformable models have many applications in dynamics, chaotic systems, and physics. Up to now, there are very few surveys works on the results of regularization in L s spaces. Our paper is the first work to investigate the inverse problem for conformable parabolic equation in such spaces. For the inverse source problem, we provide Fourier regularized solution and investigated the error between the approximate solution and the sought solution. For the backward in time problem, we also use Fourier truncation method to approximate problem. The error between the regularized solution and the exact solution is obtained in L s under some suitable assumptions on the Cauchy data.

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On an initial value problem for time fractional pseudo‐parabolic equation with Caputo derivative

Cited by 10 publications

References 26 publications

Well-posed results for nonlocal fractional parabolic equation involving Caputo-Fabrizio operator

Well-posed results for nonlocal fractional parabolic equation involving Caputo-Fabrizio operator

Semilinear parabolic diffusion systems on the sphere with Caputo-Fabrizio operator

REGULARIZATION FOR TWO INVERSE PROBLEMS FOR CONFORMABLE HEAT EQUATION IN L s SPACES

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