Fractional Calculus and Applied Analysis

Article	Citations
Sonine-Dimovski transform and spectral synthesis associated with the hyper-Bessel operator on the complex plane	41
Bounds for mixing times for finite semi-Markov processes with heavy-tail jump distribution	39
Blow-up for a non-linear stable non-Gaussian process in fractional time	31
Analysis of BURA and BURA-based approximations of fractional powers of sparse SPD matrices	29
On generalized K-functionals in $$L_p$$ for $$0<p<1$$	27
Asymptotically autonomous dynamics for fractional subcritical nonclassical diffusion equations driven by nonlinear colored noise	27
Symmetry of solutions for asymptotically symmetric nonlocal parabolic equations	27
Fractional differential equations of Bagley-Torvik and Langevin type	26
Box dimension of mixed Katugampola fractional integral of two-dimensional continuous functions	25
Differential transforms related to Caputo time-fractional derivatives and semigroups generated by fractional Schrödinger operators	24
Considerations regarding the accuracy of fractional numerical computations	24
Discrete fractional distributed Halanay inequality and applications in discrete fractional order neural network systems	23
On heat equations associated with fractional harmonic oscillators	21
Stochastic heat equation driven by space-only fractional Lévy noise	20
Rigidity of phase transitions for the fractional elliptic Gross-Pitaevskii system	20
Stability analysis of Hilfer fractional stochastic switched dynamical systems with non-Gaussian process and impulsive effects	19
Multi-parametric Le Roy function revisited	19
The Spatially Variant Fractional Laplacian	19
Towards a Unified theory of Fractional and Nonlocal Vector Calculus	19
A review of constitutive models for non-Newtonian fluids	19
Differentiation of integral Mittag-Leffler and integral Wright functions with respect to parameters	17
Fractional differential operators, fractional Sobolev spaces and fractional variation on homogeneous Carnot groups	16
Delsarte equation for Caputo operator of fractional calculus	16
Abstract multi-term fractional difference equations	15
Representations of solutions of systems of time-fractional pseudo-differential equations	15

Asymptotic analysis of three-parameter Mittag-Leffler function with large parameters, and application to sub-diffusion equation involving Bessel operator	15
Dual Spaces of Anisotropic Variable Hardy–Lorentz Spaces and Their Applications	15
On approximate controllability of multi-term time fractional measure differential equations with nonlocal conditions	14
Mixed slow-fast stochastic differential equations: Averaging principle result	14
Multi-term fractional oscillation integro-differential equations	14
A Fractional Order Derivative Newton-Raphson Method for the Computation of the Power Flow Problem Solution in Energy Systems	14
Concentration phenomenon of solutions for fractional Choquard equations with upper critical growth	13
Radial symmetry and Hopf lemma for fully nonlinear parabolic equations involving the fractional Laplacian	13
Limitations and applications in a fractional Barbalat’s Lemma	13
Two disjoint and infinite sets of solutions for a concave-convex critical fractional Laplacian equation	13
Controllability of Hilfer fractional backward evolution systems	13
Decay estimates and extinction properties for some parabolic equations with fractional time derivatives	12
On the convergence of the Galerkin method for random fractional differential equations	12
The fractional stochastic heat equation driven by time-space white noise	12
Fractional models for analysis of economic risks	11
The well-posedness analysis in Besov-type spaces for multi-term time-fractional wave equations	11
Radial symmetry and Liouville theorem for master equations	11
A high order predictor-corrector method with non-uniform meshes for fractional differential equations	11
Generalized fractional derivatives generated by Dickman subordinator and related stochastic processes	11
Fractional Wiener chaos: Part 1	11
Infinitely many sign-changing solutions for a kind of fractional Klein-Gordon-Maxwell system	10
Initial-boundary value problems for coupled systems of time-fractional diffusion equations	10
Local Existence and Non-Existence for a Fractional Reaction-Diffusion Equation in Lebesgue Spaces	10
A unified analysis framework for generalized fractional Moore–Gibson–Thompson equations: Well-posedness and singular limits	10
Properties of the Set of Admissible “State Control” Pair for a Class of Fractional Semilinear Evolution Control Systems	10
Fractional boundary value problems and elastic sticky brownian motions	10
On the Decomposition of Solutions: From Fractional Diffusion to Fractional Laplacian	10
Riemann-Liouville derivatives of abstract functions and Sobolev spaces	9
A critical elliptic problem involving exponential and singular nonlinearities	9
Controllability and observability of linear time-varying fractional systems	9
Boundedness of fractional integrals on special John–Nirenberg–Campanato and Hardy-type spaces via congruent cubes	9
On the multivariate generalized counting process and its time-changed variants	9
Integral operators defined “up to a polynomial”	9
A unified way to solve IVPs and IBVPs for the time-fractional diffusion-wave equation	9
Weighted estimates for operators of fractional integration of variable order in generalized variable Hölder spaces	9
Superlinear solutions of sublinear fractional differential equations and regular variation	9
Analysis of a fractional viscoelastic Euler-Bernoulli beam and identification of its piecewise continuous polynomial order	9
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
From time to times	8
Vallée-Poussin theorem for fractional functional differential equations	8
Abstract fractional linear pseudo-parabolic equations in Banach spaces: well-posedness, regularity, and asymptotic behavior	8
Correction: Existence, uniqueness and regularity for a semilinear stochastic subdiffusion with integrated multiplicative noise	8
Concave-convex critical problems for the spectral fractional laplacian with mixed boundary conditions	8
Analysis and Fast Approximation of a Steady-State Spatially-Dependent Distributed-order Space-Fractional Diffusion Equation	8
On the existence and uniqueness of the solution to multifractional stochastic delay differential equation	8
Fractional Musielak-Sobolev spaces: study of generalized double phase problem with Choquard-logarithmic nonlinearity	8
Filter Regularization Method for a Nonlinear Riesz-Feller Space-Fractional Backward Diffusion Problem with Temporally Dependent Thermal Conductivity	8
Summability of Formal Solutions for a Family of Generalized Moment Integro-Differential Equations	8
Convergence to logarithmic-type functions of solutions of fractional systems with Caputo-Hadamard and Hadamard fractional derivatives	8

Explicit Representation of Discrete Fractional Resolvent Families in Banach Spaces	8
Approximate solutions for fractional stochastic integro-differential equation with short memory driven by non-instantaneous impulses	7
Some nonexistence results for space–time fractional Schrödinger equations without gauge invariance	7
Multiplicity of solutions for a fractional Kirchhoff type equation with a critical nonlocal term	7
Convergence Rate Estimates for the Kernelized Predictor Corrector Method for Fractional Order Initial Value Problems	7
Numerical scheme for Erdélyi–Kober fractional diffusion equation using Galerkin–Hermite method	7
Stability and stabilization of short memory fractional differential equations with delayed impulses	7
Study on the diffusion fractional m-Laplacian with singular potential term	7
Sensitivity analysis for optimal control problems governed by Hilfer fractional differential hemivariational inequalities	7
Sequential generalized Riemann–Liouville derivatives based on distributional convolution	7
Convolution series and the generalized convolution Taylor formula	7
Robust Fractional-Order Perfect Control for Non-Full Rank Plants Described in the Grünwald-Letnikov IMC Framework	7
A semilinear diffusion PDE with variable order time-fractional Caputo derivative subject to homogeneous Dirichlet boundary conditions	7
A Strong Maximum Principle for the Fractional Laplace Equation with Mixed Boundary Condition	7
Nonlocal Kirchhoff-type problems with singular nonlinearity: existence, uniqueness and bifurcation	7
Operational matrix based numerical scheme for the solution of time fractional diffusion equations	6
Existence, nonexistence and multiplicity of bounded solutions to a nonlinear BVP associated to the fractional Laplacian	6
A second-order fitted scheme for time fractional telegraph equations involving weak singularity	6
Appell system associated with the infinite dimensional Fractional Pascal measure	6
The sliding method for fractional Laplacian systems	6
Anisotropic variable Campanato-type spaces and their Carleson measure characterizations	6
The nonlinear fractional Rayleigh-Stokes problem on an infinite interval	6
Fractional boundary value problems	6
S-asymptotically $$\omega $$-periodic solutions for time-space fractional nonlocal reaction-diffusion equation with superlinear growth nonlinear terms	6
Existence and uniqueness of a weak solution to fractional single-phase-lag heat equation	6
Monte Carlo method for fractional-order differentiation	6
A fractional version of the recursive Tau method for solving a general class of Abel-Volterra integral equations systems	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
A tempered subdiffusive Black–Scholes model	6
A fast fractional block-centered finite difference method for two-sided space-fractional diffusion equations on general nonuniform grids	6
Game-theoretical problems for fractional-order nonstationary systems	6
An inverse problem of determining the fractional order in the TFDE using the measurement at one space-time point	6
Special solutions to the space fractional diffusion problem	6
Monotonicity and uniqueness of positive solutions to elliptic fractional p-equations	6
Solving 3D fractional Schrödinger systems on the basis of Phragmén–Lindelöf methods	6
Continuous-time MISO fractional system identification using higher-order-statistics	6
Schrödinger-Maxwell equations driven by mixed local-nonlocal operators	6
On approximate controllability of semi-linear neutral integro-differential evolution systems with state-dependent nonlocal conditions	5
Non-stationary zipper $$\alpha $$-fractal functions and associated fractal operator	5
Existence and asymptotic behavior of square-mean S-asymptotically periodic solutions for fractional stochastic evolution equation with delay	5
Identifying source term and initial value simultaneously for the time-fractional diffusion equation with Caputo-like hyper-Bessel operator	5
A mutually exciting rough jump-diffusion for financial modelling	5
Subordination and memory dependent kinetics in diffusion and relaxation phenomena	5
The Cauchy problem and distribution of local fluctuations of one Riesz gravitational field	5
Variational Methods to the p-Laplacian type Nonlinear Fractional Order Impulsive Differential Equations with Sturm-Liouville Boundary-Value Problem	5
Hölder regularity for the nonlinear stochastic time-fractional slow & fast diffusion equations on $${\mathbb {R}}^d$$	5
Infinitely many large solutions to a variable order nonlocal singular equation	5
The existence and averaging principle for Caputo fractional stochastic delay differential systems	5
The fractional variation and the precise representative of $$BV^{\alpha ,p}$$ functions	5
A time-space fractional parabolic type problem: weak, strong and classical solutions	5
Sticky Brownian motions on star graphs	5
Cauchy problem for non-autonomous fractional evolution equations	5
On the three dimensional generalized Navier-Stokes equations with damping	5
Unification of popular artificial neural network activation functions	5
Reachability of time-varying fractional dynamical systems with Riemann-Liouville fractional derivative	5
Pullback dynamics of 2D non-autonomous Reissner-Mindlin-Timoshenko plate systems	5
Collage theorems, invertibility and fractal functions	5
Mixed fractional stochastic heat equation with additive fractional-colored noise	5
The Rate of Convergence on Fractional Power Dissipative Operator on Compact Manifolds	5
Hopf’s lemma and radial symmetry for the Logarithmic Laplacian problem	5
Adaptive finite-time fuzzy composite control for nonlinear fractional-order systems based on complexity avoidance	4
Existence, multiplicity and asymptotic behaviour of normalized solutions to non-autonomous fractional HLS lower critical Choquard equation	4
Global optimization of a nonlinear system of differential equations involving $$\psi $$-Hilfer fractional derivatives of complex order	4
On the existence of solutions for a class of nonlinear fractional Schrödinger-Poisson system: Subcritical and critical cases	4
Abstract fractional inverse source problem of order $$0<\alpha <1$$ in a Banach space	4
Difference Between Riesz Derivative and Fractional Laplacian on the Proper Subset of ℝ	4
Queuing models with Mittag-Leffler inter-event times	4
A new approach to multi-delay matrix valued fractional linear differential equations with constant coefficients	4
Principal curves to fractional m-Laplacian systems and related maximum and comparison principles	4
A bifurcation result for a Keller-Segel-type problem	4
Space-time fractional parabolic equations on a metric star graph with spatial fractional derivative of Sturm-Liouville type: analysis and discretization	4
Invariant tori for the fractional nonlinear Schrödinger equation with nonlinearity periodically depending on spatial variable	4
Generalized fractional operators do not preserve periodicity	4
Strong stationarity for non-smooth control problems with fractional semi-linear elliptic equations in dimension $$N\le 3$$	4
Multiplicity of couple solution for a fractional $$(\varphi , \psi )$$-like system	4
Discrete-time general fractional calculus	4
Asymptotics of the s-fractional Gaussian perimeter as $$s\rightarrow 0^+$$	4
Localized special John–Nirenberg–Campanato spaces via congruent cubes with applications to boundedness of local Calderón–Zygmund singular integrals and fractional integrals	4
Analytical solutions for fractional partial delay differential-algebraic equations with Dirichlet boundary conditions defined on a finite domain	4

Fractional differential equation on the whole axis involving Liouville derivative	4
A class of Hilfer fractional differential evolution hemivariational inequalities with history-dependent operators	4
Spectral analysis of a family of nonsymmetric fractional elliptic operators	4
Rich phenomenology of the solutions in a fractional Duffing equation	4
Attractors of Caputo fractional differential equations with triangular vector fields	4
Pricing European option under the generalized fractional jump-diffusion model	4
On the Green Function of the Killed Fractional Laplacian on the Periodic Domain	4
Existence and multiplicity of positive solutions for a critical fractional Laplacian equation with singular nonlinearity	4
On the computation of the Mittag-Leffler function of fractional powers of accretive operators	4
Comparison principles for the time-fractional diffusion equations with the Robin boundary conditions. Part I: Linear equations	4
Pointwise characterizations of variable Besov and Triebel-Lizorkin spaces via Hajłasz gradients	4
Global solutions of nonlinear fractional diffusion equations with time-singular sources and perturbed orders	4
Fractional Fokker-Planck-Kolmogorov equations with Hölder continuous drift	4
Sum of series and new relations for Mittag-Leffler functions	4
A variational theory for integral functionals involving finite-horizon fractional gradients	4
Solvability for a class of two-term nonlinear functional boundary value problems and its applications	3
Global solvability of inverse coefficient problem for one fractional diffusion equation with initial non-local and integral overdetermination conditions	3
Simulating neuronal dynamics in fractional adaptive exponential integrate-and-fire models	3
Analysis of a class of completely non-local elliptic diffusion operators	3
Applications of a new measure of noncompactness to the solvability of systems of nonlinear and fractional integral equations in the generalized Morrey spaces	3
A spectral approach to non-linear weakly singular fractional integro-differential equations	3
Topological properties of solution sets for control problems driven by fractional delay differential quasi-hemivariational inequalities and applications	3
An elementary inequality for dissipative Caputo fractional differential equations	3
Existence and uniqueness of discrete weighted pseudo S-asymptotically $$\omega $$-periodic solution to abstract semilinear superdiffusive difference equation	3
An anomalous fractional diffusion operator	3
Fractional integral operators on Orlicz slice Hardy spaces	3
Fractional Euler numbers and generalized proportional fractional logistic differential equation	3
On some even-sequential fractional boundary-value problems	3
Skellam and time-changed variants of the generalized fractional counting process	3
On the fractional Laplacian of variable order	3
Wright functions of the second kind and Whittaker functions	3
Generalized fractional Dirac type operators	3
Existence and multiplicity of solutions to magnetic Kirchhoff equations in Orlicz-Sobolev spaces	3
FCAA Related News, Events and Books (FCAA-Volume 24-5-2021)	3
Maximum Principles and Applications for Fractional Differential Equations with Operators Involving Mittag-Leffler Function	3
Computation of the inverse Mittag–Leffler function and its application to modeling ultraslow dynamics	3
Impulse response of commensurate fractional-order systems: multiple complex poles	3
Fractional vector-valued nonuniform MRA and associated wavelet packets on $$L^2\big ({\mathbb {R}},{\mathbb {C}}^M\big )$$	3
Homogenization and inverse problems for fractional diffusion equations	3
Reconstruction of a fractional evolution equation with a source	3
Representations of abstract resolvent families on time scales via Laplace Transform	3
Variable-order fractional 1-Laplacian diffusion equations for multiplicative noise removal	3
Correction: Comparison principles for the time-fractional diffusion equations with the Robin boundary conditions. Part I: Linear equations	3
On the kinetics of $$\psi $$-fractional differential equations	3
Asymptotical stabilization of fuzzy semilinear dynamic systems involving the generalized Caputo fractional derivative for $$q \in (1,2)$$	3
On the Filippov-Ważewski relaxation theorem for a certain class of fractional differential inclusions	3
An inverse problem of determining orders of systems of fractional pseudo-differential equations	3
The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces II	3
Attractors of Caputo semi-dynamical systems	3
Mixed order elliptic problems driven by a singularity, a Choquard type term and a discontinuous power nonlinearity with critical variable exponents	3
A higher order resolvent-positive finite difference approximation for fractional derivatives on bounded domains	3
Fractional order control for unstable first order processes with time delays	3
Multi-parametric Le Roy function	3
Asymptotic cycles in fractional maps of arbitrary positive orders	3
Energy stability and convergence of variable-step L1 scheme for the time fractional Swift-Hohenberg model	3
Inverse coefficient problems for the heat equation with fractional Laplacian	2
Monotone iterative technique for multi-term time fractional measure differential equations	2
Orlicz-Lorentz-Karamata Hardy martingale spaces: inequalities and fractional integral operators	2
Initial-boundary value problems for multi-term time-fractional wave equations	2
$$\psi $$-Hilfer type linear fractional differential equations with variable coefficients	2
Ground states for p-fractional Choquard-type equations with doubly or triply critical nonlinearity	2
Optimized fractional-order Butterworth filter design in complex F-plane	2
Some aspects of the contribution of Mkhitar Djrbashian to fractional calculus	2
CTRW modeling of quantum measurement and fractional equations of quantum stochastic filtering and control	2
Ground state solution for a generalized Choquard Schr$$\ddot{\text {o}}$$dinger equation with vanishing potential in homogeneous fractional Musielak Sobolev spaces	2
Approximation with continuous functions preserving fractal dimensions of the Riemann-Liouville operators of fractional calculus	2
The overdamped generalized Langevin equation with Hermite noise	2
Lump solutions of the fractional Kadomtsev–Petviashvili equation	2
Existence of positive solutions for fractional delayed evolution equations of order $$\gamma \in (1,2)$$ via measure of non-compactness	2
Local and global conserved quantities involving generalized operators	2
Convergence analysis of the time-stepping numerical methods for time-fractional nonlinear subdiffusion equations	2
Topological properties of the solution set for Caputo fractional evolution inclusions involving delay	2
An improved fractional predictor-corrector method for nonlinear fractional differential equations with initial singularity	2
On discrete tempered fractional calculus and its application	2
The similarity method and explicit solutions for the fractional space one-phase Stefan problems	2
A necessary and sufficient conditions for the global existence of solutions to fractional reaction-diffusion equations on $$\mathbb {R}^{N}$$	2
Discrete Fractional Boundary Value Problems and Inequalities	2
Least energy sign-changing solutions for fractional critical Kirchhoff–Schrödinger–Poisson with steep potential well	2
The oscillatory solutions of multi-order fractional differential equations	2
Some Properties of the Fractal Convolution of Functions	2
Fractional Sobolev type spaces of functions of two variables via Riemann-Liouville derivatives	2
Pricing Vulnerable Options in Fractional Brownian Markets: a Partial Differential Equations Approach	2
Dynamical repulsive fractional potential fields in 3D environment	2
A collection of correct fractional calculus for discontinuous functions	2
System of fractional boundary value problems at resonance	2
Existence and Controllability Results for Hilfer Fractional Evolution Equations via Integral Contractors	2
On the variable order fractional calculus of fractal interpolation functions	2
No-regret and low-regret controls of space-time fractional parabolic Sturm-Liouville equations in a star graph	2
On mild solutions of the generalized nonlinear fractional pseudo-parabolic equation with a nonlocal condition	2
Existence and regularity of mild solutions to backward problem for nonlinear fractional super-diffusion equations in Banach spaces	2
Approximate inversion for Abel integral operators of variable exponent and applications to fractional Cauchy problems	2
Final value problem for Rayleigh-Stokes type equations involving weak-valued nonlinearities	2
Multiplicity of solutions for fractional Hamiltonian systems with combined nonlinearities and without coercive conditions	2
Weighted boundedness of fractional integrals associated with admissible functions on spaces of homogeneous type	2
RETRACTED ARTICLE: Averaging principle for stochastic Caputo fractional differential equations with non-Lipschitz condition	2