Fractional Calculus and Applied Analysis

Article	Citations
Bounds for mixing times for finite semi-Markov processes with heavy-tail jump distribution	97
Mixed stochastic heat equation with fractional Laplacian and gradient perturbation	46
Considerations regarding the accuracy of fractional numerical computations	36
A review of constitutive models for non-Newtonian fluids	31
Asymptotically autonomous dynamics for fractional subcritical nonclassical diffusion equations driven by nonlinear colored noise	30
Hölder regularity for non-autonomous fractional evolution equations	26
Continuity of solutions for tempered fractional general diffusion equations driven by TFBM	26
Multivariable Fractional-Order PID Tuning by Iterative Non-Smooth Static-Dynamic H∞ Synthesis	26
Space-time fractional parabolic equations on a metric star graph with spatial fractional derivative of Sturm-Liouville type: analysis and discretization	26
Fractional Diffusion-Wave Equations: Hidden Regularity for Weak Solutions	23
Kinetic Solutions for Nonlocal Stochastic Conservation Laws	23
Some nonexistence results for space–time fractional Schrödinger equations without gauge invariance	23
Sonine-Dimovski transform and spectral synthesis associated with the hyper-Bessel operator on the complex plane	22
Error estimation of a discontinuous Galerkin method for time fractional subdiffusion problems with nonsmooth data	21
Convergence Rate Estimates for the Kernelized Predictor Corrector Method for Fractional Order Initial Value Problems	20
Global stability of fractional different orders nonlinear feedback systems with positive linear parts and interval state matrices	19
FCAA Related News, Events and Books (FCAA—volume 24–4–2021)	19
FCAA Related News, Events and Books (FCAA—volume 24–6–2021)	19
A Boundary Value Problem for a Partial Differential Equation with Fractional Derivative	17
On differentiability of solutions of fractional differential equations with respect to initial data	17
Sliding methods for the higher order fractional laplacians	16
The sliding method for fractional Laplacian systems	15
Asymptotics of the s-fractional Gaussian perimeter as $$s\rightarrow 0^+$$	14
Analysis of BURA and BURA-based approximations of fractional powers of sparse SPD matrices	14
Robust Fractional-Order Perfect Control for Non-Full Rank Plants Described in the Grünwald-Letnikov IMC Framework	14

Construction and analysis of series solutions for fractional quasi-Bessel equations	13
Study on the diffusion fractional m-Laplacian with singular potential term	13
Existence and multiplicity of positive solutions for a critical fractional Laplacian equation with singular nonlinearity	13
Multiplicity of solutions for a fractional Kirchhoff type equation with a critical nonlocal term	12
Spectral analysis of multifractional LRD functional time series	12
Subordination principle and approximation of fractional resolvents and applications to fractional evolution equations	12
Abstract fractional inverse source problem of order $$0<\alpha <1$$ in a Banach space	12
Properties of the multi-index special function $${\mathcal {W}}^{\left( \bar{\alpha },\bar{\nu }\right) }(z)$$	11
Inverse problem of determining the order of the fractional derivative in the Rayleigh-Stokes equation	11
Decay solutions to abstract impulsive fractional mobile–immobile equations involving superlinear nonlinearities	11
Discrete fractional distributed Halanay inequality and applications in discrete fractional order neural network systems	11
On generalized K-functionals in $$L_p$$ for $$0<p<1$$	11
Two-dimensional fractional shearlet transforms in $$L^2({\mathbb {R}}^2)$$	10
Time optimal controls for Hilfer fractional evolution equations	10
Nonnegative solutions of a coupled k-Hessian system involving different fractional Laplacians	10
A semilinear diffusion PDE with variable order time-fractional Caputo derivative subject to homogeneous Dirichlet boundary conditions	10
Existence and regularity of mild solutions to backward problem for nonlinear fractional super-diffusion equations in Banach spaces	10
Rigidity of phase transitions for the fractional elliptic Gross-Pitaevskii system	9
Sensitivity analysis for optimal control problems governed by Hilfer fractional differential hemivariational inequalities	9
Efficient spectral collocation method for fractional differential equation with Caputo-Hadamard derivative	9
Sensitivity analysis for a fractional stochastic differential equation with $$S^{p}$$-weighted pseudo almost periodic coefficients and infinite delay	9
Spectral analysis of a family of nonsymmetric fractional elliptic operators	9
A fractional approach to study the pure-temporal Epidemic Type Aftershock Sequence (ETAS) process for earthquakes modeling	9
On heat equations associated with fractional harmonic oscillators	8
The Spatially Variant Fractional Laplacian	8
Publisher Correction: Subordination results for a class of multi-term fractional Jeffreys-type equations	8
Transformations of the matrices of the fractional linear systems to their canonical stable forms	8
Sum of series and new relations for Mittag-Leffler functions	8
Nonlocal Kirchhoff-type problems with singular nonlinearity: existence, uniqueness and bifurcation	8
Fractional differential equations of Bagley-Torvik and Langevin type	8
Application of subordination principle to coefficient inverse problem for multi-term time-fractional wave equation	7
On the computation of the Mittag-Leffler function of fractional powers of accretive operators	7
Relative controllability of linear state-delay fractional systems	7
Simultaneous inversion for the fractional exponents in the space-time fractional diffusion equation $$\partial _t^\beta u = - {\left( { - \Delta } \right)^{\alpha /2}}u - {\left( { - \Delta } \right)^	7
A Meyer-Itô formula for stable processes via fractional calculus	7
Optimal F-domain stabilization technique for reduction of commensurate fractional-order SISO systems	7
Existence, uniqueness and regularity for a semilinear stochastic subdiffusion with integrated multiplicative noise	7
Hardy–Hénon fractional equation with nonlinearities involving exponential critical growth	7
Sequential generalized Riemann–Liouville derivatives based on distributional convolution	7
Optimal regional control for a class of semilinear time-fractional diffusion systems with distributed feedback	7
Author Correction: On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications	7
Numerical scheme for Erdélyi–Kober fractional diffusion equation using Galerkin–Hermite method	7
Monte Carlo method for fractional-order differentiation extended to higher orders	7
Numerical investigation of two models of nonlinear fractional reaction subdiffusion equations	7
Box dimension of mixed Katugampola fractional integral of two-dimensional continuous functions	7
The Bouncing Ball and the Grünwald-Letnikov Definition of Fractional Derivative	6
Overview of fractional calculus and its computer implementation in Wolfram Mathematica	6
Fractional boundary value problems	6
A bifurcation result for a Keller-Segel-type problem	6
Difference Between Riesz Derivative and Fractional Laplacian on the Proper Subset of ℝ	6

Stochastic heat equation driven by space-only fractional Lévy noise	6
Symmetry of solutions for asymptotically symmetric nonlocal parabolic equations	6
Fractional calculus for distributions	6
Existence and approximate controllability of Hilfer fractional impulsive evolution equations	6
Solving 3D fractional Schrödinger systems on the basis of Phragmén–Lindelöf methods	6
Differential transforms related to Caputo time-fractional derivatives and semigroups generated by fractional Schrödinger operators	6
A variational theory for integral functionals involving finite-horizon fractional gradients	6
On boundary value problem of the nonlinear fractional partial integro-differential equation via inverse operators	6
B-Spline Collocation Discretizations of Caputo and Riemann-Liouville Derivatives: A Matrix Comparison	6
Caputo delta weakly fractional difference equations	6
A class of Hilfer fractional differential evolution hemivariational inequalities with history-dependent operators	6
Blow-up for a non-linear stable non-Gaussian process in fractional time	6
Operational Calculus for the General Fractional Derivative and Its Applications	6
A non-local semilinear eigenvalue problem	6
Wind turbulence modeling for real-time simulation	5
A tempered subdiffusive Black–Scholes model	5
Local and global conserved quantities involving generalized operators	5
Approximate controllability results for the Sobolev type fractional delay impulsive integrodifferential inclusions of order $${r} \in (1,2)$$ via sectorial operator	5
Unified predictor–corrector method for fractional differential equations with general kernel functions	5
Regularization of an inverse source problem for fractional diffusion-wave equations under a general noise assumption	5
Fractional differential operators, fractional Sobolev spaces and fractional variation on homogeneous Carnot groups	5
Multi-parametric Le Roy function revisited	5
Fractional Fokker-Planck-Kolmogorov equations with Hölder continuous drift	5
Anniversary of Prof. S.G. Samko, FC Events (FCAA–Volume 24–2–2021)	5
Publisher Correction: Optimal approximation of analog PID controllers of complex fractional-order	5
Anisotropic variable Campanato-type spaces and their Carleson measure characterizations	5
Time-fractional discrete diffusion equation for Schrödinger operator	5
Monotonicity and uniqueness of positive solutions to elliptic fractional p-equations	5
General one-dimensional model of the time-fractional diffusion-wave equation in various geometries	5
Differentiation of integral Mittag-Leffler and integral Wright functions with respect to parameters	5
Multi-term fractional oscillation integro-differential equations	5
Stochastic solutions of generalized time-fractional evolution equations	5
Continuous-time MISO fractional system identification using higher-order-statistics	5
System of fractional boundary value problems at resonance	5
Discrete Fractional Boundary Value Problems and Inequalities	5
On the Generalized Fractional Laplacian	5
Entropy and alternative entropy functionals of fractional Gaussian noise as the functions of Hurst index	5
Numerical conservation laws of time fractional diffusion PDEs	5
Sharp asymptotics in a fractional Sturm-Liouville problem	5
Global attractivity for fractional differential equations of Riemann-Liouville type	5
Averaging Theory for Fractional Differential Equations	5
Searching for Sonin kernels	4
Principal curves to fractional m-Laplacian systems and related maximum and comparison principles	4
Asymptotic behaviour of solutions to non-commensurate fractional-order planar systems	4
Representations of solutions of systems of time-fractional pseudo-differential equations	4
Asymptotic analysis of three-parameter Mittag-Leffler function with large parameters, and application to sub-diffusion equation involving Bessel operator	4
A Fractional Order Derivative Newton-Raphson Method for the Computation of the Power Flow Problem Solution in Energy Systems	4
A time-fractional superdiffusion wave-like equation with subdiffusion possibly damping term: well-posedness and Mittag-Leffler stability	4
Mixed slow-fast stochastic differential equations: Averaging principle result	4
Delsarte equation for Caputo operator of fractional calculus	4
Strichartz’s Radon transforms for mutually orthogonal affine planes and fractional integrals	4
Rich phenomenology of the solutions in a fractional Duffing equation	4
Estimates for $$p$$-adic fractional integral operators and their commutators on $$p$$-adic mixed central Morrey spaces and generalized mixed Morrey spaces	4
Monotone iterative technique for multi-term time fractional measure differential equations	4
On approximate controllability of multi-term time fractional measure differential equations with nonlocal conditions	4
Orlicz-Lorentz-Karamata Hardy martingale spaces: inequalities and fractional integral operators	4
Fractional differential equation on the whole axis involving Liouville derivative	4
Some aspects of the contribution of Mkhitar Djrbashian to fractional calculus	4
Schrödinger-Maxwell equations driven by mixed local-nonlocal operators	4
Averaging principle for stochastic Caputo fractional differential equations with non-Lipschitz condition	4
Asymptotics of the Mittag-Leffler function $$E_a(z)$$ on the negative real axis when $$a \rightarrow 1$$	4
Dual Spaces of Anisotropic Variable Hardy–Lorentz Spaces and Their Applications	4
Three Representations of the Fractional p-Laplacian: Semigroup, Extension and Balakrishnan Formulas	4
A collection of correct fractional calculus for discontinuous functions	4
An ADMM approach to a TV model for identifying two coefficients in the time-fractional diffusion system	4
A necessary and sufficient conditions for the global existence of solutions to fractional reaction-diffusion equations on $$\mathbb {R}^{N}$$	4
An efficient numerical method to the stochastic fractional heat equation with random coefficients and fractionally integrated multiplicative noise	4
Classical versus fractional difference equations: the logistic case	4
A fast fractional block-centered finite difference method for two-sided space-fractional diffusion equations on general nonuniform grids	4
Inverse Problems for Diffusion Equation with Fractional Dzherbashian-Nersesian Operator	4
Convergence analysis of the time-stepping numerical methods for time-fractional nonlinear subdiffusion equations	4
Nehari manifold approach for fractional Kirchhoff problems with extremal value of the parameter	4
Global solutions of nonlinear fractional diffusion equations with time-singular sources and perturbed orders	3
AsymptotIc Behavior of Solutions of Fractional Differential Equations with Hadamard Fractional Derivatives	3
Stability analysis of a second-order difference scheme for the time-fractional mixed sub-diffusion and diffusion-wave equation	3
Approximate inversion for Abel integral operators of variable exponent and applications to fractional Cauchy problems	3
Self-Similar Cauchy Problems and Generalized Mittag-Leffler Functions	3
Pricing Vulnerable Options in Fractional Brownian Markets: a Partial Differential Equations Approach	3
Asymptotic behavior for a porous-elastic system with fractional derivative-type internal dissipation	3
Continuous Dependence of Fuzzy Mild Solutions on Parameters for IVP of Fractional Fuzzy Evolution Equations	3

On the variable order fractional calculus of fractal interpolation functions	3
In memory of the honorary founding editors behind the FCAA success story	3
Queuing models with Mittag-Leffler inter-event times	3
Variable-order fractional 1-Laplacian diffusion equations for multiplicative noise removal	3
Nonlinear convolution integro-differential equation with variable coefficient	3
Radial symmetry and Hopf lemma for fully nonlinear parabolic equations involving the fractional Laplacian	3
ContribUtions on Artificial Potential Field Method for Effective Obstacle Avoidance	3
Towards a Unified theory of Fractional and Nonlocal Vector Calculus	3
On the fractional Laplacian of variable order	3
The quasi-reversibility method for recovering a source in a fractional evolution equation	3
Time-dependent identification problem for a fractional Telegraph equation with the Caputo derivative	3
Operational Calculus for the Riemann–Liouville Fractional Derivative with Respect to a Function and its Applications	3
An inverse problem of determining the fractional order in the TFDE using the measurement at one space-time point	3
Concentration phenomenon of solutions for fractional Choquard equations with upper critical growth	3
Pointwise characterizations of variable Besov and Triebel-Lizorkin spaces via Hajłasz gradients	3
Fractional Wiener chaos: Part 1	3
Fractional Langevin Type Equations for White Noise Distributions	3
First order Plus Fractional Diffusive Delay Modeling: Interconnected Discrete Systems	3
Optimal feedback control for a class of fractional evolution equations with history-dependent operators	3
Abstract multi-term fractional difference equations	3
A definition of fractional k-dimensional measure: bridging the gap between fractional length and fractional area	3
An improved fractional predictor-corrector method for nonlinear fractional differential equations with initial singularity	3
Existence for a class of time-fractional evolutionary equations with applications involving weakly continuous operator	3
Identification of System with Distributed-Order Derivatives	3
Small order limit of fractional Dirichlet sublinear-type problems	3
Initial-boundary value problems for multi-term time-fractional wave equations	3
Infinitely many sign-changing solutions for a kind of fractional Klein-Gordon-Maxwell system	3
Existence of positive solutions for fractional delayed evolution equations of order $$\gamma \in (1,2)$$ via measure of non-compactness	2
Monte Carlo method for fractional-order differentiation	2
Mellin definition of the fractional Laplacian	2
S-asymptotically $$\omega $$-periodic solutions for time-space fractional nonlocal reaction-diffusion equation with superlinear growth nonlinear terms	2
On mild solutions of the generalized nonlinear fractional pseudo-parabolic equation with a nonlocal condition	2
Two disjoint and infinite sets of solutions for a concave-convex critical fractional Laplacian equation	2
Dynamical repulsive fractional potential fields in 3D environment	2
Representations of abstract resolvent families on time scales via Laplace Transform	2
A unified analysis framework for generalized fractional Moore–Gibson–Thompson equations: Well-posedness and singular limits	2
High order approximations of solutions to initial value problems for linear fractional integro-differential equations	2
Energy stability and convergence of variable-step L1 scheme for the time fractional Swift-Hohenberg model	2
Parameter identification in anomalous diffusion equations with nonlocal conditions and weak-valued nonlinearities	2
Discrete convolution operators and equations	2
Comparison principles for the time-fractional diffusion equations with the Robin boundary conditions. Part I: Linear equations	2
Radial symmetry and Liouville theorem for master equations	2
Existence and uniqueness of a weak solution to fractional single-phase-lag heat equation	2
An approximation theoretic revamping of fractal interpolation surfaces on triangular domains	2
Fractional Euler numbers and generalized proportional fractional logistic differential equation	2
Operational matrix based numerical scheme for the solution of time fractional diffusion equations	2
The Lambert function method in qualitative analysis of fractional delay differential equations	2
Localized special John–Nirenberg–Campanato spaces via congruent cubes with applications to boundedness of local Calderón–Zygmund singular integrals and fractional integrals	2
A second-order fitted scheme for time fractional telegraph equations involving weak singularity	2
Multiple positive solutions for higher-order fractional integral boundary value problems with singularity on space variable	2
Appell system associated with the infinite dimensional Fractional Pascal measure	2
Decay estimates and extinction properties for some parabolic equations with fractional time derivatives	2
Correction: Comparison principles for the time-fractional diffusion equations with the Robin boundary conditions. Part I: Linear equations	2
Lump solutions of the fractional Kadomtsev–Petviashvili equation	2
Existence of an infinite system of fractional hybrid differential equations in a tempered sequence space	2
Approximate optimal control of fractional stochastic hemivariational inequalities of order (1, 2] driven by Rosenblatt process	2
On the convergence of the Galerkin method for random fractional differential equations	2
The fractional stochastic heat equation driven by time-space white noise	2
The similarity method and explicit solutions for the fractional space one-phase Stefan problems	2
Fractional boundary value problems and elastic sticky brownian motions	2
A new approach to multi-delay matrix valued fractional linear differential equations with constant coefficients	2
Revisiting distributed order PID controller	2
Special solutions to the space fractional diffusion problem	2
A fractional version of the recursive Tau method for solving a general class of Abel-Volterra integral equations systems	2
Game-theoretical problems for fractional-order nonstationary systems	2
Skellam and time-changed variants of the generalized fractional counting process	2
Green’s Function for the Fractional KDV Equation on the Periodic Domain via Mittag-Leffler Function	2
Reconstruction of pointwise sources in a time-fractional diffusion equation	2
Analytical and dimensional properties of fractal interpolation functions on the Sierpiński gasket	2
Limitations and applications in a fractional Barbalat’s Lemma	2
Generalized fractional derivatives generated by Dickman subordinator and related stochastic processes	2
Infinitely many large solutions to a variable order nonlocal singular equation	2
Analytical solutions for fractional partial delay differential-algebraic equations with Dirichlet boundary conditions defined on a finite domain	2
The well-posedness analysis in Besov-type spaces for multi-term time-fractional wave equations	2
Global existence for three-dimensional time-fractional Boussinesq-Coriolis equations	2
Non-confluence of fractional stochastic differential equations driven by Lévy process	2
Asymptotic cycles in fractional generalizations of multidimensional maps	2
On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications	2
On some even-sequential fractional boundary-value problems	2
A high order predictor-corrector method with non-uniform meshes for fractional differential equations	2
Cauchy problem for time-space fractional incompressible Navier-Stokes equations in $$\mathbb {R}^n$$	2