A Computational Approach for the Calculation of Temperature Distribution in Casting-Mould Heterogeneous System with Fractional Order. [PDF]
Comput Math Methods Med, 2022 The purpose of this paper is to investigate the approximate solution of the casting‐mould heterogeneous system with Caputo derivative under the homotopy idea. The symmetry design of the system contains the integer partial differential equations and the fractional‐order partial differential equations. We apply Yang transform homotopy perturbation method
Luo X, Nadeem M, Asjad MI, Abdo MS.
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On Strongly Continuous Resolving Families of Operators for Fractional Distributed Order Equations
Fractal and Fractional, 2021 The aim of this work is to find by the methods of the Laplace transform the conditions for the existence of a strongly continuous resolving family of operators for a linear homogeneous equation in a Banach space with the distributed Gerasimov–Caputo ...
Vladimir E. Fedorov, Nikolay V. Filin
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Quasilinear Fractional Order Equations and Fractional Powers of Sectorial Operators
Fractal and Fractional, 2023 The fractional powers of generators for analytic operator semigroups are used for the proof of the existence and uniqueness of a solution of the Cauchy problem to a first order semilinear equation in a Banach space. Here, we use an analogous construction
Vladimir E. Fedorov +2 more
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Degenerate Multi-Term Equations with Gerasimov–Caputo Derivatives in the Sectorial Case
Mathematics, 2022 The unique solvability for the Cauchy problem in a class of degenerate multi-term linear equations with Gerasimov–Caputo derivatives in a Banach space is investigated.
Vladimir E. Fedorov, Kseniya V. Boyko
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The Regularized Mesh Scheme to Solve Quasilinear Parabolic Equation with Time-Fractional Derivative [PDF]
, 2021 A quasilinear parabolic problem with a time fractional derivative of the Caputo type and mixed boundary conditions is considered. The coefficients of the elliptic operator depend on the gradient of the solution, and this operator is uniformly monotone ...
Laitinen, E., Lapin, A. V.
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A Generalization of the Hopf-Cole Transformation [PDF]
, 2012 A generalization of the Hopf-Cole transformation and its relation to the Burgers equation of integer order and the diffusion equation with quadratic nonlinearity are discussed. The explicit form of a particular analytical solution is presented.
Miskinis, Paulius
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Fractional model of COVID-19 applied to Galicia, Spain and Portugal [PDF]
, 2023 Xunta de Galicia | Ref. ED431C 2019/02Agencia Estatal de Investigación | Ref. MTM2016-75140-PInstituto de Salud Carlos III | Ref.
Area Carracedo, Iván Carlos +4 more
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A new mathematical formulation for a phase change problem with a memory flux [PDF]
, 2018 A mathematical formulation for a one-phase change problem in a form of Stefan problem with a memory flux is obtained. The hypothesis that the integral of weighted backward fluxes is proportional to the gradient of the temperature is considered. The model
Bollati, Julieta +2 more
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Mathematics, 2020 We consider the principle of least action in the context of fractional calculus. Namely, we derive the fractional Euler–Lagrange equation and the general equation of motion with the composition of the left and right fractional derivatives defined on ...
Liana Eneeva +2 more
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Review of Some Promising Fractional Physical Models [PDF]
, 2015 Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and ...
Tarasov, Vasily E.
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