Solvability of Hyperbolic Fractional Partial Differential Equations

Akilandeeswariy, Aruchamy; Balachandran, K.; Annapoorani, N.

doi:10.11948/2017095

Cited by 9 publications

(8 citation statements)

References 22 publications

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“…This work can be considered as a contribution in the development of the traditional functional analysis method, the so called energy inequality method used to prove the well posedness of mixed problems with integral boundary conditions. For some classical cases, the reader can refeer for example to example [16,17,18,19,27], and for some fractional cases, the reader should refeer to [32,33,34,36,37,38,39,40,41]. We should also mention here that there are some important papers dealing with numerical aspects for Timoshenko systems, and having many applications, for which the reader can refer to [47 48, 49, 50].…”

Section: Introductionmentioning

confidence: 99%

On a non local non-homogeneous fractional Timoshenko system with frictional and viscoelastic damping terms

Mesloub¹,

Alhazzani²,

Gadain³

2022

Preprint

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Section: Introductionmentioning

confidence: 99%

On a non local non-homogeneous fractional Timoshenko system with frictional and viscoelastic damping terms

Mesloub¹,

Alhazzani²,

Gadain³

2022

Preprint

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“…Many natural phenomena have been modeled through partial differential equations (PDEs), especially in physics, engineering, chemistry, and biology, as well as in humanities [1,2]. A wide range of PDEs can be classified under the name of hyperbolic PDEs that have the following general form [2][3][4][5][6]: u t (x, t) a(x, t)u x (x, t) + b(x, t)u(x, t) + f (x, t), x ∈ I, t > 0, (1) subject to the following initial condition:…”

Section: Introductionmentioning

confidence: 99%

“…Several articles are interested in providing ASs to T-FPDEs of hyperbolic type, such as the Caputo time-fractional-order hyperbolic telegraph equation [30], hyperbolic T-FPDEs [31][32][33][34][35], the time-fractional diffusion equation [36], fractional advection-dispersion flow equations [37], and other hyperbolic equations. However, a limited number of research studies provided analytical and numerical solutions for hyperbolic systems of T-FPDEs.…”

Section: Introductionmentioning

confidence: 99%

A Vector Series Solution for a Class of Hyperbolic System of Caputo Time-Fractional Partial Differential Equations With Variable Coefficients

El-Ajou

Al–Zhour

2021

Front. Phys.

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In this paper, we introduce a series solution to a class of hyperbolic system of time-fractional partial differential equations with variable coefficients. The fractional derivative has been considered by the concept of Caputo. Two expansions of matrix functions are proposed and used to create series solutions for the target problem. The first one is a fractional Laurent series, and the second is a fractional power series. A new approach, via the residual power series method and the Laplace transform, is also used to find the coefficients of the series solution. In order to test our proposed method, we discuss four interesting and important applications. Numerical results are given to authenticate the efficiency and accuracy of our method and to test the validity of our obtained results. Moreover, solution surface graphs are plotted to illustrate the effect of fractional derivative arrangement on the behavior of the solution.

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“…the completion of C 0 (0, 1) for the scalar product defined by (1).The associated norm to the scalar product is given by…”

Section: Introductionmentioning

confidence: 99%

On Theoretical and Numerical Aspect of Fractional Differential Equations with Purely Integral Conditions

Brahimi¹,

Merad²,

Kılıçman³

2021

Preprint

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In this paper, we are interested in the study of a problem with fractional derivatives having boundary conditions of integral types. The problem represents a Caputo type advectiondiffusion equation where the fractional order derivative with respect to time with 1 < α < 2. The method of the energy inequalities is used to prove the existence and the uniqueness of solutions of the problem. The finite difference method is also introduced to study the problem numerically in order to find an approximate solution of the considered problem. Some numerical examples are presented to show satisfactory results.

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Solvability of Hyperbolic Fractional Partial Differential Equations

Cited by 9 publications

References 22 publications

On a non local non-homogeneous fractional Timoshenko system with frictional and viscoelastic damping terms

On a non local non-homogeneous fractional Timoshenko system with frictional and viscoelastic damping terms

A Vector Series Solution for a Class of Hyperbolic System of Caputo Time-Fractional Partial Differential Equations With Variable Coefficients

On Theoretical and Numerical Aspect of Fractional Differential Equations with Purely Integral Conditions

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