Results 21 to 30 of about 39,478 (331)
Advances in Difference Equations, 2021 We investigate the existence of solutions for a system of Riemann–Liouville fractional differential equations with nonlinearities dependent on fractional integrals, subject to coupled nonlocal boundary conditions which contain various fractional ...
Rodica Luca
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Representation of Fractional Operators Using the Theory of Functional Connections
Mathematics, 2023 This work considers fractional operators (derivatives and integrals) as surfaces f(x,α) subject to the function constraints defined by integer operators, which is a mandatory requirement of any fractional operator definition. In this respect, the problem
Daniele Mortari
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Isoperimetric problems of the calculus of variations with fractional derivatives [PDF]
, 2011 In this paper we study isoperimetric problems of the calculus of variations with left and right Riemann-Liouville fractional derivatives. Both situations when the lower bound of the variational integrals coincide and do not coincide with the lower bound ...
Agrawal +35 more
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Some fractional proportional integral inequalities
Journal of Inequalities and Applications, 2019 In the last few years, various researchers studied the so-called conformable integrals and derivatives. Based on that notion some authors used modified conformable derivatives (proportional derivatives) to generate nonlocal fractional integrals and ...
Gauhar Rahman +3 more
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Positive Solutions of a Singular Fractional Boundary Value Problem with r-Laplacian Operators
Fractal and Fractional, 2021 We investigate the existence and multiplicity of positive solutions for a system of Riemann–Liouville fractional differential equations with r-Laplacian operators and nonnegative singular nonlinearities depending on fractional integrals, supplemented ...
Alexandru Tudorache, Rodica Luca
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Numerical Approaches to Fractional Integrals and Derivatives: A Review
Mathematics, 2020 Fractional calculus, albeit a synonym of fractional integrals and derivatives which have two main characteristics—singularity and nonlocality—has attracted increasing interest due to its potential applications in the real world.
Min Cai, Changpin Li
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New classes of unified fractional integral inequalities
AIMS Mathematics, 2022 Many researchers in recent years have studied fractional integrals and derivatives. Some authors recently introduced generalized fractional integrals, the so-called unified fractional integrals.
Gauhar Rahman +4 more
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General Fractional Calculus: Multi-Kernel Approach
Mathematics, 2021 For the first time, a general fractional calculus of arbitrary order was proposed by Yuri Luchko in 2021. In Luchko works, the proposed approaches to formulate this calculus are based either on the power of one Sonin kernel or the convolution of one ...
Vasily E. Tarasov
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A fractional Gauss–Jacobi quadrature rule for approximating fractional integrals and derivatives [PDF]
Chaos, Solitons & Fractals, 2017 This is a preprint of a paper whose final and definite form is with 'Chaos, Solitons & Fractals', ISSN: 0960-0779. Submitted 1 Dec 2016; Article revised 17 Apr 2017; Article accepted for publication 19 Apr 2017; see [http://dx.doi.org/10.1016/j.chaos.2017.04.034]
Jahanshahi, S. +3 more
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Maximal Domains for Fractional Derivatives and Integrals [PDF]
Mathematics, 2020 The purpose of this short communication is to announce the existence of fractional calculi on precisely specified domains of distributions. The calculi satisfy desiderata proposed above in Mathematics 7, 149 (2019). For the desiderata (a)–(c) the examples are optimal in the sense of having maximal domains with respect to convolvability of distributions.
R. Hilfer, T. Kleiner
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