Fractional Calculus and Applied Analysis

Article	Citations
Sonine-Dimovski transform and spectral synthesis associated with the hyper-Bessel operator on the complex plane	37
Considerations regarding the accuracy of fractional numerical computations	34
Bounds for mixing times for finite semi-Markov processes with heavy-tail jump distribution	31
Asymptotically autonomous dynamics for fractional subcritical nonclassical diffusion equations driven by nonlinear colored noise	29
The Spatially Variant Fractional Laplacian	27
Fractional differential equations of Bagley-Torvik and Langevin type	26
Blow-up for a non-linear stable non-Gaussian process in fractional time	26
Analysis of BURA and BURA-based approximations of fractional powers of sparse SPD matrices	26
Symmetry of solutions for asymptotically symmetric nonlocal parabolic equations	23
On generalized K-functionals in $$L_p$$ for $$0<p<1$$	23
Box dimension of mixed Katugampola fractional integral of two-dimensional continuous functions	22
Differential transforms related to Caputo time-fractional derivatives and semigroups generated by fractional Schrödinger operators	21
Discrete fractional distributed Halanay inequality and applications in discrete fractional order neural network systems	20
Rigidity of phase transitions for the fractional elliptic Gross-Pitaevskii system	19
Stochastic heat equation driven by space-only fractional Lévy noise	19
On heat equations associated with fractional harmonic oscillators	18
Multi-parametric Le Roy function revisited	17
Multi-term fractional oscillation integro-differential equations	17
A review of constitutive models for non-Newtonian fluids	17
Asymptotic analysis of three-parameter Mittag-Leffler function with large parameters, and application to sub-diffusion equation involving Bessel operator	15
Differentiation of integral Mittag-Leffler and integral Wright functions with respect to parameters	14
Delsarte equation for Caputo operator of fractional calculus	13
Representations of solutions of systems of time-fractional pseudo-differential equations	13
Fractional differential operators, fractional Sobolev spaces and fractional variation on homogeneous Carnot groups	13
On approximate controllability of multi-term time fractional measure differential equations with nonlocal conditions	13

Dual Spaces of Anisotropic Variable Hardy–Lorentz Spaces and Their Applications	13
Mixed slow-fast stochastic differential equations: Averaging principle result	13
A Fractional Order Derivative Newton-Raphson Method for the Computation of the Power Flow Problem Solution in Energy Systems	13
Abstract multi-term fractional difference equations	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
Towards a Unified theory of Fractional and Nonlocal Vector Calculus	12
Limitations and applications in a fractional Barbalat’s Lemma	12
The fractional stochastic heat equation driven by time-space white noise	11
Fractional boundary value problems and elastic sticky brownian motions	11
On the convergence of the Galerkin method for random fractional differential equations	11
Decay estimates and extinction properties for some parabolic equations with fractional time derivatives	11
A unified analysis framework for generalized fractional Moore–Gibson–Thompson equations: Well-posedness and singular limits	11
Fractional models for analysis of economic risks	11
The well-posedness analysis in Besov-type spaces for multi-term time-fractional wave equations	10
Generalized fractional derivatives generated by Dickman subordinator and related stochastic processes	10
Infinitely many sign-changing solutions for a kind of fractional Klein-Gordon-Maxwell system	10
Fractional Wiener chaos: Part 1	10
Local Existence and Non-Existence for a Fractional Reaction-Diffusion Equation in Lebesgue Spaces	9
Radial symmetry and Liouville theorem for master equations	9
Concentration phenomenon of solutions for fractional Choquard equations with upper critical growth	9
Two disjoint and infinite sets of solutions for a concave-convex critical fractional Laplacian equation	9
A high order predictor-corrector method with non-uniform meshes for fractional differential equations	9
Superlinear solutions of sublinear fractional differential equations and regular variation	8
Properties of the Set of Admissible “State Control” Pair for a Class of Fractional Semilinear Evolution Control Systems	8
Weighted estimates for operators of fractional integration of variable order in generalized variable Hölder spaces	8
Integral operators defined “up to a polynomial”	8
Log-concavity and log-convexity of series containing multiple Pochhammer symbols	8
On the Decomposition of Solutions: From Fractional Diffusion to Fractional Laplacian	8
Riemann-Liouville derivatives of abstract functions and Sobolev spaces	8
A unified way to solve IVPs and IBVPs for the time-fractional diffusion-wave equation	8
From time to times	8
Correction: Existence, uniqueness and regularity for a semilinear stochastic subdiffusion with integrated multiplicative noise	8
Analysis of a fractional viscoelastic Euler-Bernoulli beam and identification of its piecewise continuous polynomial order	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
Concave-convex critical problems for the spectral fractional laplacian with mixed boundary conditions	8
A critical elliptic problem involving exponential and singular nonlinearities	8
Convergence to logarithmic-type functions of solutions of fractional systems with Caputo-Hadamard and Hadamard fractional derivatives	7
Explicit Representation of Discrete Fractional Resolvent Families in Banach Spaces	7
Summability of Formal Solutions for a Family of Generalized Moment Integro-Differential Equations	7
Stability and stabilization of short memory fractional differential equations with delayed impulses	7
On the existence and uniqueness of the solution to multifractional stochastic delay differential equation	7
Convolution series and the generalized convolution Taylor formula	7
Filter Regularization Method for a Nonlinear Riesz-Feller Space-Fractional Backward Diffusion Problem with Temporally Dependent Thermal Conductivity	7
Fractional Musielak-Sobolev spaces: study of generalized double phase problem with Choquard-logarithmic nonlinearity	7
Analysis and Fast Approximation of a Steady-State Spatially-Dependent Distributed-order Space-Fractional Diffusion Equation	7
Vallée-Poussin theorem for fractional functional differential equations	7
A Strong Maximum Principle for the Fractional Laplace Equation with Mixed Boundary Condition	7
Fractional-order problem coupled with a second-order Moreau’s sweeping process	7

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

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