Keywords: 34C37; 35R11; 47G20; Fractional elliptic equation; Variable-order fractional Laplacian; Variational methods;
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Keywords: Inverse problem; Fractional diffusion equation; Tikhonov regularization; Convergence analysis; 35R30; 35R11; 65M32;
Keywords: Fractional calculus; Chaos; Lyapunov exponents; Stability; Brusselator system; System of partial differential equations; Optimal homotopy asymptotic method; 26A33; 35R11; 74H10; 34H10;
Keywords: Crank-Nicolson method; variable order fractional cable equation; stability analysis; 26A33; 35R11; 65M06;
Keywords: 35R11; 65M12; Fokker-Planck equation; Caputo-Fabrizio fractional derivative; Basis functions;
Keywords: primary; 65M12; 65M06; 65M70; 35R11; Fractional diffusion equation; Fractional diffusion-wave equation; Spectral method; Stability; Convergence;
Keywords: primary; 35R11; 35J91; secondary; 35B06; 35B65; Fractional Laplacians; Positive solutions; Radial symmetry; Uniqueness; Hartree type nonlinearity; Direct methods of moving planes;
Keywords: 35R30; 35R11; 58J99; Inverse problems; Fractional diffusion equation; Partial data; Uniqueness result;
Keywords: primary; 35J65; secondary; 35B40; 35B44; 35R11; 81Q05; 82B10; Fractional Laplacian; Spatial segregation; Strongly competing systems; Entire solutions;
Keywords: primary; 35R11; 35J92; 35B33; secondary; 35A15; Brezis-Nirenberg problem; Critical growth problems; Minimization problems;
Keywords: Anomalous heat conduction; Composite material; The balance method; Inverse problem; Levenberg-Marquardt regularization; 35R11; 35R05; 65L12; 65L09;
Keywords: 35A15; 35R11; 35S05; 58E05; Fractional magnetic operators; Nehari manifold; Ljusternick-Schnirelmann Theory;
Keywords: 86A22; 74G75; 35R11; Bayesian inverse method; Fractional Helmholtz equation; Inverse scattering problem; Fractional Laplace operator;
Keywords: primary; 35R11; secondary; 35J91; 35B06; Fractional Laplacians; Odd order; Positive classical solutions; Radial symmetry; Uniqueness; Liouville theorems;
Keywords: 42B37; 42B30; 35R11; 58E20; 35B65; Fractional divergence; Fractional div-curl lemma; Fractional harmonic maps;
Keywords: primary; 35R11; 49M25; secondary; 35K05; 65N15; Nonlocal discrete diffusion equations; Fractional discrete Laplacian; Regularity and extension problem; Sobolev and Poincaré inequalities; Error of approximation; Semidiscrete heat equation;
Keywords: Navier-Stokes equations; Caputo fractional derivative; Energy methods; Approximate solutions; 35R11; 35Q30; 76D03;
Keywords: Navier-Stokes equations; Caputo fractional derivative; Cauchy problem; Sobolev space; Existence; 35R11; 35Q30; 46E35;
Keywords: Time fractional systems of partial differential equations; Riemann-Liouville fractional derivative; Conservation laws; Nonlinear self-adjointness; 26A33; 34A08; 35R11; 76M60; 70S10;
Keywords: primary; 35R11; 35C15; secondary; 45N05; Materials with memory; Subdiffusion quasilinear equations; Caputo derivative; A priori estimates;
Keywords: 35R11; 35J20; 35J65; 35J61; Fractional Laplacian; Convex and concave nonlinearities; Threshold value;
Keywords: primary; 35R11; 35J62; secondary; 35A15; Fractional p-Laplacian; Variational methods; Singular nonlinearity;
Keywords: Fractional convection-reaction-diffusion equation; Variable coefficient; Compact difference method; Richardson extrapolation; High-order convergence; 65M06; 65M12; 65M15; 35R11;
Keywords: 35R11; 47G20; 60G52; 42C15; 47D07; 58C40; Fractional operators; Continuous frames; Non-self-adjoint integro-differential operators; Markov semigroups; Reflected stable processes; Spectral theory;
Keywords: 35R30; 35R11; 35B50; Inverse source problem; Fractional diffusion equation; Harnack's inequality; Strong maximum principle;
Keywords: primary; 35R11; secondary; 45K05; 35C15; 47G20; Nonlocal diffusion; Riemann-Liouville derivative; Fractional Laplacian; Decay of solutions; Energy inequality; Fundamental solution;
Keywords: 49Q05; 35R11; 53A10; Nonlocal minimal surfaces; Boundary regularity; Barriers;
Keywords: 35A02; 35B30; 35B35; 35B53; 35D30; 35J15; 35K59; 35K65; 35L65; 35R09; 35R11; Uniqueness; Distributional solutions; Nonlinear degenerate diffusion; Porous medium equation; Stefan problem; Fractional Laplacian; Nonlocal operators; Existence; Stability; Loca
Keywords: primary; 53C21; secondary; 35R11; 53A30; Fractional Yamabe problem; Blow-up analysis;
Keywords: 35R11; 35A01; Fractional Laplacian system; Method of moving planes; Radial symmetry;
Keywords: 35R11; 65F60; 65M06; 65N22Vorticity-stream function formulation; Splitting method
Keywords: 35R11; 35J61; 35R06; Fractional Laplacian; Radon measure; Dirac mass; Singularities;
Keywords: 35B32; 35C07; 35J20; 35R09; 35R11; 45G05; 47G10Allen–Cahn equation; Morse index; Variational method; Mountain pass solution
Keywords: 35B33; 35C20; 35K58; 35R11; 78A35; 82D37Drift–diffusion equation; Fractional dissipation; Large-time behavior
Keywords: 35R11; 65M06; 65M12Fractional differential equation; Caputo derivative; Diffusion equation; Implicit finite difference method; Distributed order equation
Keywords: Weighted pseudo almost automorphic functions; Two-term fractional order differential equations; Sectorial operator; Regularized family; Mild solutions34A08; 35R11; 47D06; 45N05
Keywords: 35R11; 35A15; 35J60Integro-differential operators; Fractional Laplacian; Kirchhoff type equations; Fountain Theorem; Dual Fountain Theorem
Keywords: 35B45; 35R11; 35K55Fractional Laplacian; Symmetrization; Nonlocal parabolic equations; Comparison theorems; Best constants
Keywords: 35R11; 65M06; 65N30Multi-term time fractional diffusion-wave equations; High order compact finite difference; Galerkin spectral method; Solvability; Energy method; Convergence and stability
Keywords: 35R11; 35Q35; 82C70Transport equation; Nonlocal velocity; Fractional dissipation
Keywords: 35R11; 35J61; 35R06Fractional Laplacian; Radon measure; Dirac measure; Green kernel; Bessel capacities
Keywords: 5J20; 35Q55; 35B38; 35R11; Variational methods; Polynomial decay; Fractional Laplacian; Choquard equations;
Keywords: 35R11; 35B40; 35K45; Drift-diffusion-Poisson system; Fractional dissipation; Self-similar asymptotics; Large-time behavior;
A high-order L2-compact difference method for Caputo-type time-fractional sub-diffusion equations with variable coefficients
Keywords: Fractional sub-diffusion equation; Variable coefficient; Compact difference method; High-order convergence; Energy method; 65M06; 65M12; 65M15; 35R11;
On the solution of time-fractional KdV-Burgers equation using Petrov-Galerkin method for propagation of long wave in shallow water
Keywords: Fractional KdV-Burgers equation; Petrov-Galerkin method; B-spline; Grünwald-Letnikov fractional derivative; 26A33; 35G25; 35R11; 35Q35; 42C40;
New solutions of fractional Drinfeld-Sokolov-Wilson system in shallow water waves
Keywords: Fractional Drinfeld-Sokolov-Wilson system; Shallow water waves; Conformable fractional derivative; Perturbation iteration algorithm; Sine-Gordon expansion method; 35R11; 35A20; 35C05;
Local RBF-FD technique for solving the two-dimensional modified anomalous sub-diffusion equation
Keywords: Riemann-Liouville fractional derivative; RBF-FD method; Finite difference scheme; Stability analysis; Convergence analysis; Energy method; 65M70; 35R11;
Lie symmetry approach for The Vlasov-Maxwell system of equations
Keywords: 34A08; 35R11; 26A33; 58D19; 70S10; Fractional integro-differential equation; Fractional derivative; Lie symmetry; Invariant solution;
The fractional Schrödinger equation with Hardy-type potentials and sign-changing nonlinearities
Keywords: 35Q55; 35A15; 35J20; 35R11; 58E05; Ground state; Variational methods; Nehari manifold; Fractional Schrödinger equation; Periodic and localized potentials; Hardy inequality; Sign-changing nonlinearity;
Multi-bump solutions for fractional Nirenberg problem
Keywords: 35R11; 35B25; 35B33; Fractional partial differential equations; Lyapunov-Schmidt reduction; Critical exponents;