A class of time-fractional Dirac type operators

Băleanu, Dumitru; Restrepo, Joel E.; Сураган, Дурвудхан

doi:10.1016/j.chaos.2020.110590

Cited by 24 publications

(23 citation statements)

References 27 publications

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“…Many generalizations are obtained in this direction. For example, fractional Dirac operator on Cliord algebras are investigated in the papers [6,7]. In the cited papers showed that the fractional action-like variational approach constructed to model weak dissipative dynamical systems may have interesting features when applied on classical eld theory.…”

Section: Introductionmentioning

confidence: 99%

Differentiable functions in a three-dimensional associative noncommutative algebra

Kuzmenko

Shpakivskyi

2022

Advances in the Theory of Nonlinear Analysis and Its Application

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We consider a three-dimensional associative noncommutative algebra A 2 over the eld C with the basis {I 1 , I 2 , ρ}, where I 1 , I 2 are idempotents and ρ is nilpotent. The algebra A 2 contains the algebra of bicomplex numbers B(C) as a subalgebra. In this paper we consider functions of the formwhere ξ 1 , ξ 2 , ξ 3 are independent complex variables and f 1 , f 2 , f 3 are holomorphic functions of three complex variables. We construct in an explicit form all functions dened by equalities dΦ = dζ •Φ (ζ) or dΦ = Φ (ζ)•dζ. The obtained descriptions we apply to representation of the mentioned class of functions by series. Also we established integral representations of these functions.

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Section: Introductionmentioning

confidence: 99%

Differentiable functions in a three-dimensional associative noncommutative algebra

Kuzmenko

Shpakivskyi

2022

Advances in the Theory of Nonlinear Analysis and Its Application

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“…The development of a fractional hyperholomorphic function theory represents a very recent topic of research, see [5-7, 19, 29, 41] and the references given there. In particular, the interest for considering fractional Laplace and Dirac Operator is devoted in [1,2,8,9].…”

Section: Introductionmentioning

confidence: 99%

“…[g](ξ, τ )ie iθ K β 2 ,β 3 a (τ, q) j K α θ,a (τ, q)σ θ τ = 1 2 [ K α 0 ,α 1 a (τ, q)(dτ [2] ∧ dτ ) − K α 2 ,α 3 a (τ, q)ie −iθ (dτ [1] ∧ dτ ) ] + 1 2 [−K α 0 ,α 1 a (τ, q)ie iθ (dτ [1] ∧ dτ ) + K α 2 ,α 3 a (τ, q)(dτ [2] ∧ dτ ) ]j σ θ τ K β θ,a (τ, q) = 1 2 [ (dτ [2] ∧ dτ )K β 0 ,β 1 a (τ, q) + ie iθ (dτ [1] ∧ dτ )K β 2 ,β 3 a (τ, q) ] + 1 2 [ −ie iθ (dτ [1] ∧ dτ )K β 0 ,β 1 a (τ, q) + (dτ [2] ∧ dτ )K β 2 ,β 3 a (τ, q) ]j Corollary 3.11. Let α = (α 0 , α 1 , α 2 , α 3 ), β = (β 0 , β 1 , β 2 , β 3 ) ∈ C(i) 4 with 0 < ℜα ℓ , ℜβ ℓ < 1 for ℓ = 0, 1, 2, 3 and f, g ∈ AC 1 (J b a , C(i)).…”

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confidence: 99%

A fractional Borel-Pompeiu type formula for holomorphic functions of two complex variables

González-Cervantes,

Bory-Reyes

2021

Preprint

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The present paper is a continuation of our work [11], where we introduced a fractional operator calculus related to a fractional ψ−Fueter operator in the one-dimensional Riemann-Liouville derivative sense in each direction of the quaternionic structure, that depends on an additional vector of complex parameters with fractional real parts.This allowed us also to study a pair of lower order fractional operators and prove the associated analogues of both Stokes and Borel-Pompieu formulas for holomorphic functions in two complex variables.

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“…Fractional hyperholomorphic function theory is a very recent topic of research, see [4,6,7,10,11,16,20,28] for more details. In particular, the interest for considering fractional Laplace and Dirac type operators is devoted in [1,2,8,9,21].…”

Section: Introductionmentioning

confidence: 99%

A quaternionic perturbed fractional $ψ-$Fueter operator calculus

González-Cervantes¹,

Reyes²

2021

Preprint

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Quaternionic analysis offers a function theory focused on the concept of ψ−hyperholomorphic functions defined as null solutions of the ψ−Fueter operator, where ψ is an arbitrary orthogonal base (called structural set) of H 4 .The main goal of the present paper is to extend the results given in [12], where a fractional ψ−hyperholomorphic function theory was developed. We introduce a quaternionic perturbed fractional ψ−Fueter operator calculus, where Stokes and Borel-Pompeiu formulas in this perturbed fractional ψ−Fueter setting are presented.

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A class of time-fractional Dirac type operators

Cited by 24 publications

References 27 publications

Differentiable functions in a three-dimensional associative noncommutative algebra

Differentiable functions in a three-dimensional associative noncommutative algebra

A fractional Borel-Pompeiu type formula for holomorphic functions of two complex variables

A quaternionic perturbed fractional $ψ-$Fueter operator calculus

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