Analytical solution of a Maxwell fluid with slip effects in view of the Caputo-Fabrizio derivative⋆

Asif, Naseer Ahmad; Hammouch, Zakia; Riaz, Muhammad Bilal

doi:10.1140/epjp/i2018-12098-6

Cited by 61 publications

(25 citation statements)

References 25 publications

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“…Especially in recent years, many important theoretical results and applications have been obtained with the CFO and ABO. Some interesting studies such as [17,10,2,3,18,25,24,8] have been resulted in the sense of the CFO.…”

Section: Mehmet Yavuz and Necati Ozdemirmentioning

confidence: 99%

See 1 more Smart Citation

Comparing the new fractional derivative operators involving exponential and Mittag-Leffler kernel

Yavuz¹,

Özdemir²

2020

Discrete &Amp; Continuous Dynamical Systems - S

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In this manuscript, we have proposed a comparison based on newly defined fractional derivative operators which are called as Caputo-Fabrizio (CF) and Atangana-Baleanu (AB). In 2015, Caputo and Fabrizio established a new fractional operator by using exponential kernel. After one year, Atangana and Baleanu recommended a different-type fractional operator that uses the generalized Mittag-Leffler function (MLF). Many real-life problems can be modelled and can be solved by numerical-analytical solution methods which are derived with these operators. In this paper, we suggest an approximate solution method for PDEs of fractional order by using the mentioned operators. We consider the Laplace homotopy transformation method (LHTM) which is the combination of standard homotopy technique (SHT) and Laplace transformation method (LTM). In this study, we aim to demonstrate the effectiveness of the aforementioned method by comparing the solutions we have achieved with the exact solutions. Furthermore, by constructing the error analysis, we test the practicability and usefulness of the method.

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Section: Mehmet Yavuz and Necati Ozdemirmentioning

confidence: 99%

“…with the same initial and boundary conditions as in Eqs. (8) and (9), respectively. By using the LT of the ABO as we defined in Eq.…”

Section: Mehmet Yavuz and Necati Ozdemirmentioning

confidence: 99%

Comparing the new fractional derivative operators involving exponential and Mittag-Leffler kernel

Yavuz¹,

Özdemir²

2020

Discrete &Amp; Continuous Dynamical Systems - S

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“…The CF derivative [15], given in the above definitions, has been recently used in the mathematical modeling of HBV [21], Maxwell fluid with slip effects [26], and diabetes model [27].…”

Section: Definitionmentioning

confidence: 99%

“…Proof Since all the functions S H (t), E H (t), I H (t) and S V (t), E V (t), I V (t) are bounded, we have shown that the kernels fulfill the Lipschitz condition, thus on using of Eqs. (25) and (26) and by using the recursive method, we obtain the succeeding relation as follows:…”

Section: Theoremmentioning

confidence: 99%

A fractional order pine wilt disease model with Caputo–Fabrizio derivative

et al. 2018

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A Caputo-Fabrizio type fractional order mathematical model for the dynamics of pine wilt disease (FPWD) is presented. The basic properties of the model are investigated. The existence and uniqueness of the solution for the proposed FPWD model are given via the fixed point theorem. The numerical simulations for the model are obtained by using particular parameter values. The non-integer order derivative provides more flexible and deeper information about the complexity of the dynamics of the proposed FPWD model than the integer order models established before.

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“…In the last two years, many authors used Caputo-Fabrizio fractional derivative operator in many interesting models and with many known methods, see [11][12][13][14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

An Alternative Approach for Nonlinear Optimization Problem with Caputo - Fabrizio Derivative

Evirgen

Yavuz

2018

ITM Web Conf.

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In this study, a fractional mathematical model with steepest descent direction is proposed to find optimal solutions for a class of nonlinear programming problem. In this sense, Caputo-Fabrizio derivative is adapted to the mathematical model. To demonstrate the solution trajectory of the mathematical model, we use the multistage variational iteration method (MVIM). Numerical simulations and comparisons on some test problems show that the mathematical model generated using Caputo-Fabrizio fractional derivative is both feasible and efficient to find optimal solutions for a certain class of equality constrained optimization problems.

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Analytical solution of a Maxwell fluid with slip effects in view of the Caputo-Fabrizio derivative⋆

Cited by 61 publications

References 25 publications

Comparing the new fractional derivative operators involving exponential and Mittag-Leffler kernel

Comparing the new fractional derivative operators involving exponential and Mittag-Leffler kernel

A fractional order pine wilt disease model with Caputo–Fabrizio derivative

An Alternative Approach for Nonlinear Optimization Problem with Caputo - Fabrizio Derivative

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