Geometrical study and solutions for family of burgers-like equation with fractional order space time

Abdel-Salam, Emad A.-B.; Jazmati, M. S.; Ahmad, Harith

doi:10.1016/j.aej.2021.06.032

Cited by 10 publications

(7 citation statements)

References 52 publications

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“…Nonlinear and linear fractional models show essential roles in applied science. In the last two decades, several scientists and researchers have been interested in seeking a numerical and analytical solution to fractional differential equations [69][70][71][72][73][74][75][76].…”

Section: List Of Symbolsmentioning

confidence: 99%

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MHD Casson Nanofluid Flow over Convectively Heated Non-Linear via a Porous Medium: Fractional Order Analysis Based on an Extending Surface with Suction/Injection

Abdelhafez,

Abd-Alla,

Abo-Dahab

et al. 2024

Preprint

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An attempt is made to explain the thermophysical properties of the viscoelastic fluid flow generated by a stretched, nonlinearized surface. Here, the Casson fluid model characterizes viscoelasticity, which is then rheologically stated in the fractional momentum equation. The characteristics of Casson fluid flow are carefully examined in a transversally magnetized field with the option of suction or injection to the surface. Porousness is another attribute of flow medium. To illustrate the change in heat transmission inside the flow domain, convective heating is applied to the surface. To find out how well thermophoretic forces and Brownian motion affect particle diffusion, nanosized particles are suspended in the Cassin fluid. Mass transport measurements are also taken into account for generative chemical reactions. Flow-narrating fractional differential equations for a problem are first obtained in fractional differential equations and then, through the use of similarity, transformed into an fractional ordinary differential coupled system. Through graphical structures, variations in flow-associated distributions against relevant parameters are revealed. Additionally computed are wall drag, heat, and mass fluxes. By comparing the computed results to previously released data in a limited sense, the computing results' credibility is verified.

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Section: List Of Symbolsmentioning

confidence: 99%

“…Nonlinear fractional dynamical systems can describe a wide range of scientific problems. Many researchers have conducted many studies on these systems to understand the features of these problems in real applications [69][70][71][72][73][74][75][76]. Nonlinear and linear fractional models show essential roles in applied science.…”

Section: List Of Symbolsmentioning

confidence: 99%

MHD Casson Nanofluid Flow over Convectively Heated Non-Linear via a Porous Medium: Fractional Order Analysis Based on an Extending Surface with Suction/Injection

Abdelhafez,

Abd-Alla,

Abo-Dahab

et al. 2024

Preprint

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show abstract

“…Recently, a study of convergence analysis for nonlinear perturbed systems of delay differential equations and nonlinear parameterized problems has been treated as a new approach (see previous works [45,46]). Note that the conformable fractional derivative can be obtained from differentiable and non-differentiable functions, which have many applications in continuous and non-continuous media in the literature [39,41,44,47] and references therein.…”

Section: Complex Conformable Hasse Derivative Basesmentioning

confidence: 99%

On the convergence of series of fractional Hasse derivative bases in Fréchet spaces

Zayed,

Hassan,

Abdel‐Salam

2024

Math Methods in App Sciences

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This paper introduces a generalization of the Hasse derivative in the sense of the complex conformable derivative. The definition coincides with the classical version of the Hasse derivative of order . Accordingly, a new base, named complex conformable Hasse derivative bases (CCHDBs), is defined. We investigate the existence of expansions of analytic functions in a series of CCHDBs in Fréchet space on closed and open disks, open regions surrounding closed disks, for all entire functions and at the origin. Moreover, an upper bound for the order and type of the CCHDBs is obtained and proved to be attainable. The ‐property of CCHDBs is also discussed. Our results improve and extend the analog results in the complex analysis related to the classical complex derivative of a base of polynomials (BPs). The obtained results clarify several implications for the CCHDBs of special functions such as Euler, Bernoulli, Chebyshev, Bessel, and Gontcharaff polynomials.

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“…Remark The two definitions (10) and (12) are the extension of conformable fractional derivative and integral defined by Khalil et al, 27 which has many application in physics, mathematical problems, plasma, astronomy, and engineering; see, for example, previous works 36,38,55–58 and reference therein. Furthermore, there are several applications of the two definitions (10) and (12) in the theory of conformal complex analysis, see previous studies 30–33 …”

Section: Complex Conformable Fractional Derivative and Integral Basesmentioning

confidence: 99%

Approximation of functions by complex conformable derivative bases in Fréchet spaces

Hassan

Abdel-Salam

Rashwan

2022

Math Methods in App Sciences

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In the present paper, the representation, in different domains, of analytic functions by complex conformable fractional derivative bases (CCFDB) and complex conformable fractional integral bases (CCFIB) in Fréchet space are investigated.Results are proved to show that such representation is possible in closed disks, open disks, open regions surrounding closed disks, at the origin, and for all entire functions. Also, some results concerning the growth order and type of CCFDB and CCFIB are determined. Moreover, the T 𝜌 -property of CCFDB and CCFIB is discussed. The obtained results recover some known results when 𝛼 = 1.Finally, some applications to the CCFDB and CCFIB of Bernoulli, Euler, Bessel, and Chebyshev polynomials have been studied.

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Geometrical study and solutions for family of burgers-like equation with fractional order space time

Cited by 10 publications

References 52 publications

MHD Casson Nanofluid Flow over Convectively Heated Non-Linear via a Porous Medium: Fractional Order Analysis Based on an Extending Surface with Suction/Injection

MHD Casson Nanofluid Flow over Convectively Heated Non-Linear via a Porous Medium: Fractional Order Analysis Based on an Extending Surface with Suction/Injection

On the convergence of series of fractional Hasse derivative bases in Fréchet spaces

Approximation of functions by complex conformable derivative bases in Fréchet spaces

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