Rheological analysis of the general fractional-order viscoelastic model involving the Miller–Ross kernel
Sign Up to like & getrecommendations! Published in 2021 at "Acta Mechanica"
DOI: 10.1007/s00707-021-02994-7
Abstract: The present work is mainly stimulated by the definition of the general fractional-order derivative operator (GFODO) involving the Miller–Ross kernel in the sense of the Liouville–Sonine type. The novel emphasis is the introduction of the… read more here.
Keywords: miller ross; order; general fractional; model ... See more keywords
On General Fractional Differential Inclusions with Nonlocal Integral Boundary Conditions
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DOI: 10.1007/s12591-016-0319-5
Abstract: This paper investigates the existence of solutions for fractional differential inclusions involving Caputo fractional derivative of any order together with nonlocal integral boundary conditions. Our study includes the cases when the multivalued map involved in… read more here.
Keywords: fractional differential; general fractional; differential inclusions; integral boundary ... See more keywords
Anomalous diffusion equation using a new general fractional derivative within the Miller–Ross kernel
Sign Up to like & getrecommendations! Published in 2020 at "Modern Physics Letters B"
DOI: 10.1142/s0217984920502899
Abstract: In view of the generalization of Miller–Ross kernel in the sense of Riemann–Liouville type, we propose the new definitions of the general fractional integral (GFI) and general fractional derivative... read more here.
Keywords: miller ross; general fractional; ross kernel; fractional derivative ... See more keywords
Operational calculus for the general fractional derivative and its applications
Sign Up to like & getrecommendations! Published in 2021 at "Fractional Calculus and Applied Analysis"
DOI: 10.1515/fca-2021-0016
Abstract: Abstract In this paper, we first address the general fractional integrals and derivatives with the Sonine kernels that possess the integrable singularities of power function type at the point zero. Both particular cases and compositions… read more here.
Keywords: derivative applications; calculus general; fractional derivative; operational calculus ... See more keywords
A new general fractional-order derivative with Rabotnov fractional-exponential kernel
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DOI: 10.2298/tsci180825254y
Abstract: In this article, a general fractional-order derivative of the Riemann-Liouville type with the non-singular kernel involving the Rabotnov fractional-exponential function is addressed for the first time. A new general fractional-order derivative model for the anomalous… read more here.
Keywords: fractional exponential; general fractional; order derivative; fractional order ... See more keywords
Multi-Kernel General Fractional Calculus of Arbitrary Order
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DOI: 10.3390/math11071726
Abstract: An extension of the general fractional calculus (GFC) of an arbitrary order, proposed by Luchko, is formulated. This extension is also based on a multi-kernel approach, in which the Laplace convolutions of different Sonin kernels… read more here.
Keywords: general fractional; fractional calculus; arbitrary order; kernel general ... See more keywords
Solution of the Generalized Burgers Equation Using Homotopy Perturbation Method with General Fractional Derivative
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DOI: 10.3390/sym15030634
Abstract: This research paper introduces the generalized Burgers equation, a mathematical model defined using the general fractional derivative, the most recent operator in fractional calculus. The general fractional derivative can be reduced into three well-known operators,… read more here.
Keywords: general fractional; burgers equation; fractional derivative; perturbation method ... See more keywords