Quantitative functional calculus in Sobolev spaces by Carlo Morosi, Livio Pizzocchero

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Further Developments of Bessel Functions via Conformable Calculus with Applications by Mahmoud Abul-Ez, Mohra Zayed, Ali Youssef

“…The provided algorithm may be beneficial to enrich the Bessel function theory via fractional calculus.…”
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Discrete Mittag-Leffler Functions in Linear Fractional Difference Equations by Jan Čermák, Tomáš Kisela, Luděk Nechvátal

“…This paper investigates some initial value problems in discrete fractional calculus. We introduce a linear difference equation of fractional order along with suitable initial conditions of fractional type and prove the existence and uniqueness of the solution. …”
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Differential Calculus on N-Graded Manifolds by G. Sardanashvily, W. Wachowski

“…The differential calculus, including formalism of linear differential operators and the Chevalley–Eilenberg differential calculus, over N-graded commutative rings and on N-graded manifolds is developed. …”
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A local meshless radial basis functions based method for solving fractional integral equations by Mehdi Radmanesh, Mohammad Ebadi

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Elements of mathematical phenomenology and analogies of electrical and mechanical oscillators of the fractional type with finite number of degrees of freedom of oscillations: linea... by Katica R. (Stevanović) Hedrih, Gradimir V. Milovanović

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Fractal Continuum Maxwell Creep Model by Andriy Kryvko, Claudia del C. Gutiérrez-Torres, José Alfredo Jiménez-Bernal, Orlando Susarrey-Huerta, Eduardo Reyes de Luna, Didier Samayoa

“…This methodology employs local fractional differential operators on discontinuous properties of fractal sets embedded in the integer space-time so that they behave as analytic envelopes of non-analytic functions in the fractal continuum space-time. Then, creep strain <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ε</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula>, creep modulus <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>J</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula>, and relaxation compliance <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>G</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula> in materials with fractal linear viscoelasticity can be described by their generalized forms, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>ε</mi><mi>β</mi></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mspace width="0.166667em"></mspace><msup><mi>J</mi><mi>β</mi></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mrow><mi> </mi><mi>and</mi><mi> </mi></mrow><msup><mi>G</mi><mi>β</mi></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi><mo>=</mo><mi>d</mi><mi>i</mi><mi>m</mi><mi>S</mi><mo>/</mo><mi>d</mi><mi>i</mi><mi>m</mi><mi>H</mi></mrow></semantics></math></inline-formula> represents the time fractal dimension, and it implies the variable-order of fractality of the self-similar domain under study, which are <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mi>i</mi><mi>m</mi><mi>S</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mi>i</mi><mi>m</mi><mi>H</mi></mrow></semantics></math></inline-formula> for their spectral and Hausdorff dimensions, respectively. …”
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Probability Density Evolution Algorithm for Stochastic Dynamical Systems Based on Fractional Calculus by Yang Yan, Xiaohong Yu

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Analytic solutions of a generalized complex multi-dimensional system with fractional order by Baleanu Dumitru, Ibrahim Rabha W.

“…The Duhamel principle is a mathematical principle that allows us to solve linear partial differential equations. This system is generalized by the concept of the kk-symbol fractional calculus. …”
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Metric-affine cosmological models and the inverse problem of the calculus of variations. Part II: Variational bootstrapping of the $$\Lambda $$ Λ CDM model by Ludovic Ducobu, Nicoleta Voicu

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Backward Continuation of the Solutions of the Cauchy Problem for Linear Fractional System with Deviating Argument by Hristo Kiskinov, Mariyan Milev, Milena Petkova, Andrey Zahariev

“…This work considers a Cauchy (initial) problem for a linear delayed system with derivatives in Caputo’s sense of incommensurate order, distributed delays, and piecewise initial functions. …”
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On the Existence and Uniqueness Results for Fuzzy Linear and Semilinear Fractional Evolution Equations Involving Caputo Fractional Derivative by Ali El Mfadel, Said Melliani, M’hamed Elomari

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On the finite Fourier transforms of functions with infinite discontinuities by Branko Saric

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On Discrete Fractional Integral Inequalities for a Class of Functions by Saima Rashid, Hijaz Ahmad, Aasma Khalid, Yu-Ming Chu

“…Based on the theory of discrete fractional calculus, explicit bounds for a class of positive functions nn∈ℕ concerned are established. …”
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Convexity of Certain q-Integral Operators of p-Valent Functions by K. A. Selvakumaran, S. D. Purohit, Aydin Secer, Mustafa Bayram

“…By applying the concept (and theory) of fractional q-calculus, we first define and introduce two new q-integral operators for certain analytic functions defined in the unit disc 𝒰. …”
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Numerical Approach Based on Two-Dimensional Fractional-Order Legendre Functions for Solving Fractional Differential Equations by Qingxue Huang, Fuqiang Zhao, Jiaquan Xie, Lifeng Ma, Jianmei Wang, Yugui Li

“…The principal characteristic of the approach is the new orthogonal functions based on shifted Legendre polynomials to the fractional calculus. …”
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Mathematical model and its solution for water-altering-gas (WAG) injection process incorporating the effect of miscibility, gravity, viscous fingering and permeability heterogeneit... by Mohammad Yunus Khan

“…The model was generated in the form of a quasi-linear first-order partial differential equation, which was solved analytically in two dimensions (2-D) utilizing vector calculus. …”
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Blind equalization algorithm based on complex support vector regression by Ling YANG, Liang CHEN, Bin ZHAO, Guolong ZHANG, Yuan LI

“…A new blind equalization algorithm for complex valued signals was proposed based on the framework of complex support vector regression(CSVR).In the proposed algorithm,the error function of multi-modulus algorithm (MMA) was substituted into CSVR to construct the cost function,and the regression relationship was established by widely linear estimation,and the equalizer coefficients were determined by the iterative re-weighted least square (IRWLS) method.Different from spliting the complex valued signals into real valued signals used in support vector regression,the Wirtinger’s calculus was used in complex support vector regression to analyze the complex signals directly in the complex regenerative kernel Hilbert space.Simulation experiments show that for QPSK modulated signals,compared with the blind equalization algorithm based on support vector regression,the equalization performance of the proposed algorithm is significantly improved in linear channel and nonlinear channel by choosing appropriate kernel function and iterative optimization method.…”
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Phase-lag mixed integral equation of a generalized symmetric potential kernel and its physical meanings in (3+1) dimensions by Azhar Rashad Jan

“…The position kernel was imposed, according to Hooke's law, as a generalized potential function in L2(Ω). By applying the properties of fractional calculus, it is possible to get an integro-differential Fredholm-Volterra integral equation (Io-DF-VIE). …”
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Analytic Normalized Solutions of 2D Fractional Saint-Venant Equations of a Complex Variable by Najla M. Alarifi, Rabha W. Ibrahim

“…We formulate the extended operator in a linear convolution operator with a normalized function to study some important geometric behaviors. …”
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