Hybrid functions approach for the fractional Riccati differential equation

Maleknejad, K.; Torkzadeh, Leila

doi:10.2298/fil1609453m

Cited by 10 publications

(4 citation statements)

References 23 publications

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“…Models such as chromo-natural inflation [30] organize the gauge field under SU (2) to maintain isotropy and spatial homogeneity, though other group structures are feasible. But all * Electronic address: avery.tishue.gr@dartmouth.edu such models share a common feature: the tensor shear due to the gauge field vev strongly affects GW amplification and evolution during inflation [45][46][47][48][49][50][51][52][53][54][55][56]. The upshot is that these models overwrite the standard inflationary expressions that connect the primordial tensor amplitude to the scale of inflation or the tensor tilt to the slow roll parameters.…”

Section: Introductionmentioning

confidence: 99%

Relic cosmological vector fields and inflationary gravitational waves

Tishue

Caldwell

2021

Phys. Rev. D

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We show that relic vector fields can significantly impact a spectrum of primordial gravitational waves in the post-inflationary era. We consider a triplet of U(1) fields in a homogeneous, isotropic configuration. The interaction between the gravitational waves and the vector fields, from the end of reheating to the present day, yields novel spectral features. The amplitude, tilt, shape, and net chirality of the gravitational wave spectrum are shown to depend on the abundance of the electric-and magnetic-like vector fields. Our results show that even a modest abundance can have strong implications for efforts to detect the imprint of gravitational waves on the cosmic microwave background polarization. We find that a vector field comprising less than 2% of the energy density during the radiation dominated era can have a greater than order unity effect on the predicted inflationary gravitational wave spectrum.

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Section: Introductionmentioning

confidence: 99%

Relic cosmological vector fields and inflationary gravitational waves

Tishue

Caldwell

2021

Phys. Rev. D

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“…In [21], numerical solution of boundary value problem of fractional Bagley-Torvik equation is given in the reproducing kernel space. In [14], the authors study the numerical approach based on operational matrices of fractional differential equations with a hybrid of block-pulse functions and Chebyshev polynomials. The existence of positive and negative solutions and properties of their derivatives for the generalized Bagley-Torvik fractional differential equation is given in [24].…”

Section: Introductionmentioning

confidence: 99%

An exponential spline approximation for fractional Bagley–Torvik equation

Emadifar

Jalilian

2020

Bound Value Probl

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In this paper, we approximate the solution of fractional Bagley-Torvik equation by using the exponential spline function and the shifted Grünwald difference operator. The proposed methods reduce to the system of algebraic equations. The convergence analysis of the methods has been discussed. The numerical examples are presented to illustrate the applications of the methods and to compare the computed results with the other methods.

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“…Therefore, the development of effective and easy‐to‐use numerical schemes for solving such equations acquires an increasing interest. While several numerical techniques have been proposed to solve many different problems (see, for instance [22–49], and references therein), there have been few research studies that developed numerical methods to solve DOFDEs (see [50–58]). The development, however, for efficient numerical methods to solve DOFDEs is still an important issue [51].…”

Section: Introductionmentioning

confidence: 99%

Numerical solutions of distributed order fractional differential equations in the time domain using the Müntz–Legendre wavelets approach

Maleknejad

Rashidinia

Eftekhari

2020

Numerical Methods Partial

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In this paper, a numerical method is presented to obtain and analyze the behavior of numerical solutions of distributed order fractional differential equations of the general form in the time domain with the Caputo fractional derivative. The suggested method is based on the Müntz-Legendre wavelet approximation. We derive a new operational vector for the Riemann-Liouville fractional integral of the Müntz-Legendre wavelets by using the Laplace transform method. Applying this operational vector and collocation method in our approach, the problem can be reduced to a system of linear and nonlinear algebraic equations. The arising system can be solved by the Newton method. Discussion on the error bound and convergence analysis for the proposed method is presented. Finally, seven test problems are considered to compare our results with other well-known methods used for solving these problems. The results in the tabulated tables highlighted that the proposed method is an efficient mathematical tool for analyzing distributed order fractional differential equations of the general form.

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Hybrid functions approach for the fractional Riccati differential equation

Cited by 10 publications

References 23 publications

Relic cosmological vector fields and inflationary gravitational waves

Relic cosmological vector fields and inflationary gravitational waves

An exponential spline approximation for fractional Bagley–Torvik equation

Numerical solutions of distributed order fractional differential equations in the time domain using the Müntz–Legendre wavelets approach

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