Fractional Calculus and Applied Analysis

Article	Citations
Sonine-Dimovski transform and spectral synthesis associated with the hyper-Bessel operator on the complex plane	39
Considerations regarding the accuracy of fractional numerical computations	34
Bounds for mixing times for finite semi-Markov processes with heavy-tail jump distribution	31
Blow-up for a non-linear stable non-Gaussian process in fractional time	29
Analysis of BURA and BURA-based approximations of fractional powers of sparse SPD matrices	27
Fractional differential equations of Bagley-Torvik and Langevin type	27
On generalized K-functionals in $$L_p$$ for $$0<p<1$$	26
Symmetry of solutions for asymptotically symmetric nonlocal parabolic equations	26
Box dimension of mixed Katugampola fractional integral of two-dimensional continuous functions	24
Differential transforms related to Caputo time-fractional derivatives and semigroups generated by fractional Schrödinger operators	23
Rigidity of phase transitions for the fractional elliptic Gross-Pitaevskii system	22
Discrete fractional distributed Halanay inequality and applications in discrete fractional order neural network systems	22
On heat equations associated with fractional harmonic oscillators	21
Stability analysis of Hilfer fractional stochastic switched dynamical systems with non-Gaussian process and impulsive effects	20
A review of constitutive models for non-Newtonian fluids	19
Asymptotically autonomous dynamics for fractional subcritical nonclassical diffusion equations driven by nonlinear colored noise	19
The Spatially Variant Fractional Laplacian	18
Multi-parametric Le Roy function revisited	18
Stochastic heat equation driven by space-only fractional Lévy noise	18
Differentiation of integral Mittag-Leffler and integral Wright functions with respect to parameters	17
Delsarte equation for Caputo operator of fractional calculus	15
On approximate controllability of multi-term time fractional measure differential equations with nonlocal conditions	15
Mixed slow-fast stochastic differential equations: Averaging principle result	15
A Fractional Order Derivative Newton-Raphson Method for the Computation of the Power Flow Problem Solution in Energy Systems	14
Multi-term fractional oscillation integro-differential equations	13

Representations of solutions of systems of time-fractional pseudo-differential equations	13
Asymptotic analysis of three-parameter Mittag-Leffler function with large parameters, and application to sub-diffusion equation involving Bessel operator	13
Dual Spaces of Anisotropic Variable Hardy–Lorentz Spaces and Their Applications	13
Towards a Unified theory of Fractional and Nonlocal Vector Calculus	13
Abstract multi-term fractional difference equations	13
Fractional differential operators, fractional Sobolev spaces and fractional variation on homogeneous Carnot groups	13
Radial symmetry and Hopf lemma for fully nonlinear parabolic equations involving the fractional Laplacian	12
Initial-boundary value problems for coupled systems of time-fractional diffusion equations	12
Fractional boundary value problems and elastic sticky brownian motions	12
Infinitely many sign-changing solutions for a kind of fractional Klein-Gordon-Maxwell system	11
Decay estimates and extinction properties for some parabolic equations with fractional time derivatives	11
On the convergence of the Galerkin method for random fractional differential equations	11
Concentration phenomenon of solutions for fractional Choquard equations with upper critical growth	11
Two disjoint and infinite sets of solutions for a concave-convex critical fractional Laplacian equation	11
The fractional stochastic heat equation driven by time-space white noise	11
Fractional models for analysis of economic risks	10
Fractional Wiener chaos: Part 1	10
Generalized fractional derivatives generated by Dickman subordinator and related stochastic processes	10
The well-posedness analysis in Besov-type spaces for multi-term time-fractional wave equations	10
Limitations and applications in a fractional Barbalat’s Lemma	10
A high order predictor-corrector method with non-uniform meshes for fractional differential equations	10
Radial symmetry and Liouville theorem for master equations	9
Controllability of Hilfer fractional backward evolution systems	9
On the Decomposition of Solutions: From Fractional Diffusion to Fractional Laplacian	9
Local Existence and Non-Existence for a Fractional Reaction-Diffusion Equation in Lebesgue Spaces	9
Analysis of a fractional viscoelastic Euler-Bernoulli beam and identification of its piecewise continuous polynomial order	9
A unified analysis framework for generalized fractional Moore–Gibson–Thompson equations: Well-posedness and singular limits	9
Properties of the Set of Admissible “State Control” Pair for a Class of Fractional Semilinear Evolution Control Systems	9
A unified way to solve IVPs and IBVPs for the time-fractional diffusion-wave equation	9
Integral operators defined “up to a polynomial”	8
A critical elliptic problem involving exponential and singular nonlinearities	8
Superlinear solutions of sublinear fractional differential equations and regular variation	8
Log-concavity and log-convexity of series containing multiple Pochhammer symbols	8
Fractional-order problem coupled with a second-order Moreau’s sweeping process	8
Abstract fractional linear pseudo-parabolic equations in Banach spaces: well-posedness, regularity, and asymptotic behavior	8
Boundedness of fractional integrals on special John–Nirenberg–Campanato and Hardy-type spaces via congruent cubes	8
Controllability and observability of linear time-varying fractional systems	8
From time to times	8
Correction: Existence, uniqueness and regularity for a semilinear stochastic subdiffusion with integrated multiplicative noise	8
Summability of Formal Solutions for a Family of Generalized Moment Integro-Differential Equations	8
Concave-convex critical problems for the spectral fractional laplacian with mixed boundary conditions	8
Weighted estimates for operators of fractional integration of variable order in generalized variable Hölder spaces	8
On the multivariate generalized counting process and its time-changed variants	8
Riemann-Liouville derivatives of abstract functions and Sobolev spaces	8
Filter Regularization Method for a Nonlinear Riesz-Feller Space-Fractional Backward Diffusion Problem with Temporally Dependent Thermal Conductivity	8
Fractional Musielak-Sobolev spaces: study of generalized double phase problem with Choquard-logarithmic nonlinearity	8
Vallée-Poussin theorem for fractional functional differential equations	7
Robust Fractional-Order Perfect Control for Non-Full Rank Plants Described in the Grünwald-Letnikov IMC Framework	7
Analysis and Fast Approximation of a Steady-State Spatially-Dependent Distributed-order Space-Fractional Diffusion Equation	7
On the existence and uniqueness of the solution to multifractional stochastic delay differential equation	7

Stability and stabilization of short memory fractional differential equations with delayed impulses	7
The sliding method for fractional Laplacian systems	7
A Strong Maximum Principle for the Fractional Laplace Equation with Mixed Boundary Condition	7
Explicit Representation of Discrete Fractional Resolvent Families in Banach Spaces	7
Approximate solutions for fractional stochastic integro-differential equation with short memory driven by non-instantaneous impulses	7
Convolution series and the generalized convolution Taylor formula	7
Convergence to logarithmic-type functions of solutions of fractional systems with Caputo-Hadamard and Hadamard fractional derivatives	7
Convergence Rate Estimates for the Kernelized Predictor Corrector Method for Fractional Order Initial Value Problems	6
Anisotropic variable Campanato-type spaces and their Carleson measure characterizations	6
A semilinear diffusion PDE with variable order time-fractional Caputo derivative subject to homogeneous Dirichlet boundary conditions	6
Continuous-time MISO fractional system identification using higher-order-statistics	6
Nonlocal Kirchhoff-type problems with singular nonlinearity: existence, uniqueness and bifurcation	6
Some nonexistence results for space–time fractional Schrödinger equations without gauge invariance	6
An efficient numerical method to the stochastic fractional heat equation with random coefficients and fractionally integrated multiplicative noise	6
Multiplicity of solutions for a fractional Kirchhoff type equation with a critical nonlocal term	6
Study on the diffusion fractional m-Laplacian with singular potential term	6
A tempered subdiffusive Black–Scholes model	6
Sensitivity analysis for optimal control problems governed by Hilfer fractional differential hemivariational inequalities	6
Sequential generalized Riemann–Liouville derivatives based on distributional convolution	6
Schrödinger-Maxwell equations driven by mixed local-nonlocal operators	6
Numerical scheme for Erdélyi–Kober fractional diffusion equation using Galerkin–Hermite method	6
Solving 3D fractional Schrödinger systems on the basis of Phragmén–Lindelöf methods	6
B-Spline Collocation Discretizations of Caputo and Riemann-Liouville Derivatives: A Matrix Comparison	6
Monotonicity and uniqueness of positive solutions to elliptic fractional p-equations	5
S-asymptotically $$\omega $$-periodic solutions for time-space fractional nonlocal reaction-diffusion equation with superlinear growth nonlinear terms	5
Infinitely many large solutions to a variable order nonlocal singular equation	5
Hölder regularity for the nonlinear stochastic time-fractional slow & fast diffusion equations on $${\mathbb {R}}^d$$	5
On approximate controllability of semi-linear neutral integro-differential evolution systems with state-dependent nonlocal conditions	5
Existence, nonexistence and multiplicity of bounded solutions to a nonlinear BVP associated to the fractional Laplacian	5
Special solutions to the space fractional diffusion problem	5
An inverse problem of determining the fractional order in the TFDE using the measurement at one space-time point	5
The nonlinear fractional Rayleigh-Stokes problem on an infinite interval	5
Sharp asymptotics in a fractional Sturm-Liouville problem	5
A fractional version of the recursive Tau method for solving a general class of Abel-Volterra integral equations systems	5
Existence and uniqueness of a weak solution to fractional single-phase-lag heat equation	5
Existence and asymptotic behavior of square-mean S-asymptotically periodic solutions for fractional stochastic evolution equation with delay	5
Approximate calculation of the Caputo-type fractional derivative from inaccurate data. Dynamical approach	5
Unification of popular artificial neural network activation functions	5
A fast fractional block-centered finite difference method for two-sided space-fractional diffusion equations on general nonuniform grids	5
A second-order fitted scheme for time fractional telegraph equations involving weak singularity	5
Fractional boundary value problems	5
Game-theoretical problems for fractional-order nonstationary systems	5
On the three dimensional generalized Navier-Stokes equations with damping	5
Variational Methods to the p-Laplacian type Nonlinear Fractional Order Impulsive Differential Equations with Sturm-Liouville Boundary-Value Problem	5
Non-stationary zipper $$\alpha $$-fractal functions and associated fractal operator	5
Monte Carlo method for fractional-order differentiation	5
Appell system associated with the infinite dimensional Fractional Pascal measure	5
Operational matrix based numerical scheme for the solution of time fractional diffusion equations	5
Multi-term fractional integro-differential equations in power growth function spaces	4
Reachability of time-varying fractional dynamical systems with Riemann-Liouville fractional derivative	4
The Cauchy problem and distribution of local fluctuations of one Riesz gravitational field	4
Global optimization of a nonlinear system of differential equations involving $$\psi $$-Hilfer fractional derivatives of complex order	4
A bifurcation result for a Keller-Segel-type problem	4
Global stability of fractional different orders nonlinear feedback systems with positive linear parts and interval state matrices	4
Short time coupled fractional fourier transform and the uncertainty principle	4
Existence, multiplicity and asymptotic behaviour of normalized solutions to non-autonomous fractional HLS lower critical Choquard equation	4
A time-space fractional parabolic type problem: weak, strong and classical solutions	4
Cauchy problem for non-autonomous fractional evolution equations	4
The existence and averaging principle for Caputo fractional stochastic delay differential systems	4
Identifying source term and initial value simultaneously for the time-fractional diffusion equation with Caputo-like hyper-Bessel operator	4
Collage theorems, invertibility and fractal functions	4
Multiplicity of couple solution for a fractional $$(\varphi , \psi )$$-like system	4
The fractional variation and the precise representative of $$BV^{\alpha ,p}$$ functions	4
Spectral analysis of a family of nonsymmetric fractional elliptic operators	4
Pricing European option under the generalized fractional jump-diffusion model	4
An efficient localized collocation solver for anomalous diffusion on surfaces	4
On the Green Function of the Killed Fractional Laplacian on the Periodic Domain	4
On the existence of solutions for a class of nonlinear fractional Schrödinger-Poisson system: Subcritical and critical cases	4
Sticky Brownian motions on star graphs	4
Hopf’s lemma and radial symmetry for the Logarithmic Laplacian problem	4
Pullback dynamics of 2D non-autonomous Reissner-Mindlin-Timoshenko plate systems	4
Subordination and memory dependent kinetics in diffusion and relaxation phenomena	4
Attractors of Caputo fractional differential equations with triangular vector fields	4
Existence and multiplicity of positive solutions for a critical fractional Laplacian equation with singular nonlinearity	4
Abstract fractional inverse source problem of order $$0<\alpha <1$$ in a Banach space	4
On the computation of the Mittag-Leffler function of fractional powers of accretive operators	4
Discrete-time general fractional calculus	4
A mutually exciting rough jump-diffusion for financial modelling	4
Strong stationarity for non-smooth control problems with fractional semi-linear elliptic equations in dimension $$N\le 3$$	4
Mixed fractional stochastic heat equation with additive fractional-colored noise	4

The Rate of Convergence on Fractional Power Dissipative Operator on Compact Manifolds	4
A new approach to multi-delay matrix valued fractional linear differential equations with constant coefficients	3
Comparison principles for the time-fractional diffusion equations with the Robin boundary conditions. Part I: Linear equations	3
Solvability for a class of two-term nonlinear functional boundary value problems and its applications	3
Homogenization and inverse problems for fractional diffusion equations	3
Asymptotic cycles in fractional maps of arbitrary positive orders	3
Maximum Principles and Applications for Fractional Differential Equations with Operators Involving Mittag-Leffler Function	3
Attractors of Caputo semi-dynamical systems	3
Energy stability and convergence of variable-step L1 scheme for the time fractional Swift-Hohenberg model	3
On the fractional Laplacian of variable order	3
Queuing models with Mittag-Leffler inter-event times	3
Skellam and time-changed variants of the generalized fractional counting process	3
Fractional Fokker-Planck-Kolmogorov equations with Hölder continuous drift	3
Sum of series and new relations for Mittag-Leffler functions	3
Simultaneous inversion for the fractional exponents in the space-time fractional diffusion equation $$\partial _t^\beta u = - {\left( { - \Delta } \right)^{\alpha /2}}u - {\left( { - \Delta } \right)^	3
Localized special John–Nirenberg–Campanato spaces via congruent cubes with applications to boundedness of local Calderón–Zygmund singular integrals and fractional integrals	3
Global solutions of nonlinear fractional diffusion equations with time-singular sources and perturbed orders	3
Wright functions of the second kind and Whittaker functions	3
Mixed order elliptic problems driven by a singularity, a Choquard type term and a discontinuous power nonlinearity with critical variable exponents	3
Global solvability of inverse coefficient problem for one fractional diffusion equation with initial non-local and integral overdetermination conditions	3
Fractional differential equation on the whole axis involving Liouville derivative	3
An anomalous fractional diffusion operator	3
Müntz sturm-liouville problems: Theory and numerical experiments	3
On some even-sequential fractional boundary-value problems	3
Representations of abstract resolvent families on time scales via Laplace Transform	3
Analytical solutions for fractional partial delay differential-algebraic equations with Dirichlet boundary conditions defined on a finite domain	3
Fractional order control for unstable first order processes with time delays	3
A variational theory for integral functionals involving finite-horizon fractional gradients	3
Space-time fractional parabolic equations on a metric star graph with spatial fractional derivative of Sturm-Liouville type: analysis and discretization	3
Asymptotics of the s-fractional Gaussian perimeter as $$s\rightarrow 0^+$$	3
Principal curves to fractional m-Laplacian systems and related maximum and comparison principles	3
Correction: Comparison principles for the time-fractional diffusion equations with the Robin boundary conditions. Part I: Linear equations	3
A spectral approach to non-linear weakly singular fractional integro-differential equations	3
On the kinetics of $$\psi $$-fractional differential equations	3
An elementary inequality for dissipative Caputo fractional differential equations	3
Asymptotical stabilization of fuzzy semilinear dynamic systems involving the generalized Caputo fractional derivative for $$q \in (1,2)$$	3
Variable-order fractional 1-Laplacian diffusion equations for multiplicative noise removal	3
Impulse response of commensurate fractional-order systems: multiple complex poles	3
Pointwise characterizations of variable Besov and Triebel-Lizorkin spaces via Hajłasz gradients	3
Fractional Euler numbers and generalized proportional fractional logistic differential equation	3
Rich phenomenology of the solutions in a fractional Duffing equation	3
Invariant tori for the fractional nonlinear Schrödinger equation with nonlinearity periodically depending on spatial variable	3
A class of Hilfer fractional differential evolution hemivariational inequalities with history-dependent operators	3
Difference Between Riesz Derivative and Fractional Laplacian on the Proper Subset of ℝ	3
Generalized fractional Dirac type operators	2
Hardy–Hénon fractional equation with nonlinearities involving exponential critical growth	2
Optimal regional control for a class of semilinear time-fractional diffusion systems with distributed feedback	2
Existence and multiplicity of solutions to magnetic Kirchhoff equations in Orlicz-Sobolev spaces	2
Relative controllability of linear state-delay fractional systems	2
FCAA Related News, Events and Books (FCAA-Volume 24-5-2021)	2
Properties of the multi-index special function $${\mathcal {W}}^{\left( \bar{\alpha },\bar{\nu }\right) }(z)$$	2
Multi-parametric Le Roy function	2
Reconstruction of a fractional evolution equation with a source	2
A Meyer-Itô formula for stable processes via fractional calculus	2
On mild solutions of the generalized nonlinear fractional pseudo-parabolic equation with a nonlocal condition	2
Monotone iterative technique for multi-term time fractional measure differential equations	2
A collection of correct fractional calculus for discontinuous functions	2
Existence and Controllability Results for Hilfer Fractional Evolution Equations via Integral Contractors	2
System of fractional boundary value problems at resonance	2
The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces II	2
Nehari manifold approach for fractional Kirchhoff problems with extremal value of the parameter	2
Discrete Fractional Boundary Value Problems and Inequalities	2
Fractional vector-valued nonuniform MRA and associated wavelet packets on $$L^2\big ({\mathbb {R}},{\mathbb {C}}^M\big )$$	2
Hölder regularity for non-autonomous fractional evolution equations	2
An inverse problem of determining orders of systems of fractional pseudo-differential equations	2
On differentiability of solutions of fractional differential equations with respect to initial data	2
Computation of the inverse Mittag–Leffler function and its application to modeling ultraslow dynamics	2
Decay solutions to abstract impulsive fractional mobile–immobile equations involving superlinear nonlinearities	2
A higher order resolvent-positive finite difference approximation for fractional derivatives on bounded domains	2
Existence, uniqueness and regularity for a semilinear stochastic subdiffusion with integrated multiplicative noise	2
Time optimal controls for Hilfer fractional evolution equations	2
Dynamical repulsive fractional potential fields in 3D environment	2
Approximate inversion for Abel integral operators of variable exponent and applications to fractional Cauchy problems	2
No-regret and low-regret controls of space-time fractional parabolic Sturm-Liouville equations in a star graph	2
Some aspects of the contribution of Mkhitar Djrbashian to fractional calculus	2
On discrete tempered fractional calculus and its application	2
Strichartz’s Radon transforms for mutually orthogonal affine planes and fractional integrals	2
Subordination principle and Feynman-Kac formulae for generalized time-fractional evolution equations	2
Local and global conserved quantities involving generalized operators	2
Numerical investigation of two models of nonlinear fractional reaction subdiffusion equations	2
Analysis of a class of completely non-local elliptic diffusion operators	2
Discrete fractional-order Halanay inequality with mixed time delays and applications in discrete fractional-order neural network systems	2
Applications of a new measure of noncompactness to the solvability of systems of nonlinear and fractional integral equations in the generalized Morrey spaces	2
Author Correction: On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications	2
Existence and uniqueness of discrete weighted pseudo S-asymptotically $$\omega $$-periodic solution to abstract semilinear superdiffusive difference equation	2
Mixed stochastic heat equation with fractional Laplacian and gradient perturbation	2
Fractional integral operators on Orlicz slice Hardy spaces	2
On the Filippov-Ważewski relaxation theorem for a certain class of fractional differential inclusions	2
Existence and regularity of mild solutions to backward problem for nonlinear fractional super-diffusion equations in Banach spaces	2
Convergence analysis of the time-stepping numerical methods for time-fractional nonlinear subdiffusion equations	2
Orlicz-Lorentz-Karamata Hardy martingale spaces: inequalities and fractional integral operators	2
Variational methods for nonpositive mixed local–nonlocal operators	2
A necessary and sufficient conditions for the global existence of solutions to fractional reaction-diffusion equations on $$\mathbb {R}^{N}$$	2
Fractional Diffusion-Wave Equations: Hidden Regularity for Weak Solutions	2
General one-dimensional model of the time-fractional diffusion-wave equation in various geometries	2