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Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 12/2018, Volume 117, pp. 117 - 124
Journal Article
Ricerche di Matematica, ISSN 0035-5038, 12/2019, Volume 68, Issue 2, pp. 661 - 677
This paper establishes the Hardy–Littlewood–Pólya inequalities, the Hardy inequalities and the Hilbert inequalities on amalgam spaces. Moreover, it also gives... 
Integral operator | 26D10 | Probability Theory and Stochastic Processes | Hardy inequality | Mathematics | Amalgam spaces | Mellin convolution | Geometry | 42B35 | Algebra | 44A05 | Analysis | Numerical Analysis | Hilbert inequality | 46E30 | Mathematics, general | Hausdorff operator | 26D15 | Hadamard fractional integral
Journal Article
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 06/2018, Volume 59, pp. 608 - 611
This short note analyses the Caputo–Fabrizio operator. It is verified that it does not fit the usual concepts neither for fractional nor for integer... 
Caputo-Fabrizio operator | Fractional derivative | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL | Electrical engineering | Analysis
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 02/2016, Volume 270, Issue 4, pp. 1416 - 1478
We consider a class of non-uniformly nonlinear elliptic equations whose model is given by where and , and establish the related nonlinear Calderón–Zygmund... 
Degenerate operators | Non-uniform ellipticity | Regularity | Calderón–Zygmund estimates | Calderón-Zygmund estimates | EQUATIONS | Calderon-Zygmund estimates | Q-GROWTH | GRADIENT | MINIMIZERS | MATHEMATICS | INTEGRAL FUNCTIONALS | PARABOLIC-SYSTEMS | VARIATIONAL-PROBLEMS | WEAK SOLUTIONS | FRACTIONAL SOBOLEV SPACES
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 10/2013, Volume 66, Issue 7, pp. 1245 - 1260
We analyze a nonlocal diffusion operator having as special cases the fractional Laplacian and fractional differential operators that arise in several... 
Nonlocal vector calculus | Fractional Laplacian | Finite element methods | Nonlocal diffusion | Fractional Sobolev spaces | Nonlocal operators | MATHEMATICS, APPLIED | TRANSPORT | APPROXIMATION | EQUATIONS | DYNAMICS
Journal Article
Integral Equations and Operator Theory, ISSN 0378-620X, 11/2011, Volume 71, Issue 3, pp. 327 - 355
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 01/2014, Volume 94, pp. 156 - 170
In this paper we show the existence of non-negative solutions for a Kirchhoff type problem driven by a nonlocal integrodifferential operator, that is where is... 
Fractional Laplacian | Vibrating string | Kirchhoff equation | Fractional | Laplacian | MATHEMATICS, APPLIED | MINIMAL-SURFACES | MULTIPLICITY | EQUATIONS | MATHEMATICS | ELLIPTIC PROBLEMS | R-N | CRITICAL GROWTH | DYNAMIC BOUNDARY-CONDITIONS | SYSTEMS | Nonlinearity
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2020, Volume 482, Issue 1, p. 123523
Let be a Schrödinger operator on the Heisenberg group , where is the sublaplacian on and the nonnegative potential belongs to the reverse Hölder class with .... 
Reverse Hölder class | Heisenberg group | Morrey spaces | Fractional integral operators | Schrödinger operator | Adams inequality | MATHEMATICS | MATHEMATICS, APPLIED | COMPLEX | WEIGHTED INEQUALITIES | EQUATIONS | Schrodinger operator | COMMUTATORS | Reverse Holder class
Journal Article
INDIANA UNIVERSITY MATHEMATICS JOURNAL, ISSN 0022-2518, 2018, Volume 67, Issue 1, pp. 293 - 327
We describe a set of conformally covariant boundary operators associated to the Paneitz operator, in the sense that they give rise to a conformally covariant... 
MATHEMATICS | Poincare-Einstein manifold | CONSTANT MEAN-CURVATURE | boundary operator | Conformally covariant operator | DETERMINANTS | fractional Laplacian | MANIFOLDS | Sobolev trace inequality | SCALAR-FLAT METRICS | SOBOLEV
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 04/2019, Volume 77, Issue 8, pp. 2130 - 2144
A new operator splitting method is proposed for American options under time-fractional Black–Scholes models. The fractional linear complementarity problem is... 
Operator splitting | Black–Scholes | Order of convergence | American option | Linear complementarity problem | Fractional calculus | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | APPROXIMATION | Black-Scholes | DOUBLE-BARRIER OPTIONS | African Americans | Analysis | Methods | Splitting | Mathematical models | Convolution
Journal Article
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 09/2016, Volume 38, pp. 178 - 191
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 09/2017, Volume 481, pp. 276 - 283
In this paper, a new fractional operator of variable order with the use of the monotonic increasing function is proposed in sense of Caputo type. The... 
Fourier transform | Laplace transform | Fractional derivative of variable-order | Anomalous diffusion | PHYSICS, MULTIDISCIPLINARY | EQUATION | Electrical engineering | Rock mechanics | Physics - Statistical Mechanics
Journal Article
Fractional Calculus and Applied Analysis, ISSN 1311-0454, 02/2017, Volume 20, Issue 1, pp. 7 - 51
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 06/2019, Volume 474, Issue 1, pp. 94 - 115
This work studies the fractional maximal operator acting between Orlicz spaces. The necessary and sufficient conditions for the existence of optimal target and... 
Fractional maximal operator | Reduction theorem | Optimality | Orlicz spaces | MATHEMATICS | MATHEMATICS, APPLIED | SOBOLEV EMBEDDINGS | INEQUALITIES | Mathematics - Functional Analysis
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 09/2018, Volume 505, pp. 688 - 706
We presented an analysis of evolutions equations generated by three fractional derivatives namely the Riemann–Liouville, Caputo–Fabrizio and the... 
Non-markovian process | Semi-group principle | Markovian process | Evolution equations | Fractional derivatives | PHYSICS, MULTIDISCIPLINARY | Markov processes | Water, Underground | Organic farming | Laws, regulations and rules | Analysis
Journal Article