Fractional Calculus and Applied Analysis

Article	Citations
Sonine-Dimovski transform and spectral synthesis associated with the hyper-Bessel operator on the complex plane	49
On generalized K-functionals in $$L_p$$ for $$0<p<1$$	39
Symmetry of solutions for asymptotically symmetric nonlocal parabolic equations	35
Asymptotically autonomous dynamics for fractional subcritical nonclassical diffusion equations driven by nonlinear colored noise	34
Rigidity of phase transitions for the fractional elliptic Gross-Pitaevskii system	33
Considerations regarding the accuracy of fractional numerical computations	31
Differential transforms related to Caputo time-fractional derivatives and semigroups generated by fractional Schrödinger operators	30
Stochastic heat equation driven by space-only fractional Lévy noise	29
The Spatially Variant Fractional Laplacian	27
Blow-up for a non-linear stable non-Gaussian process in fractional time	26
Bernstein Fractional Derivatives: Censoring and Stochastic Processes	23
Stability analysis of Hilfer fractional stochastic switched dynamical systems with non-Gaussian process and impulsive effects	22
Analysis of BURA and BURA-based approximations of fractional powers of sparse SPD matrices	22
The generalized Duhamel principle for fully coupled systems of fractional order	21
A review of constitutive models for non-Newtonian fluids	20
On heat equations associated with fractional harmonic oscillators	19
Discrete fractional distributed Halanay inequality and applications in discrete fractional order neural network systems	19
Fractional differential equations of Bagley-Torvik and Langevin type	19
Fractional differential operators, fractional Sobolev spaces and fractional variation on homogeneous Carnot groups	18
Mixed slow-fast stochastic differential equations: Averaging principle result	18
Direct and inverse abstract Cauchy problems with fractional powers of almost sectorial operators	17
Fractal Riemann-Stieltjes Calculus	17
Dual Spaces of Anisotropic Variable Hardy–Lorentz Spaces and Their Applications	17
Multi-parametric Le Roy function revisited	16
A Fractional Order Derivative Newton-Raphson Method for the Computation of the Power Flow Problem Solution in Energy Systems	16

Abstract multi-term fractional difference equations	15
Differentiation of integral Mittag-Leffler and integral Wright functions with respect to parameters	15
Multi-term fractional oscillation integro-differential equations	15
Asymptotic analysis of three-parameter Mittag-Leffler function with large parameters, and application to sub-diffusion equation involving Bessel operator	15
On the convergence of the Galerkin method for random fractional differential equations	14
On approximate controllability of multi-term time fractional measure differential equations with nonlocal conditions	14
Decay estimates and extinction properties for some parabolic equations with fractional time derivatives	14
Representations of solutions of systems of time-fractional pseudo-differential equations	14
Inverse t-Source problem and a strict positivity property for coupled subdiffusion systems	14
Correction to: A nonuniform and fast two-grid L1-FEM algorithm for nonlinear multi-term time-fractional diffusion equation and its robust error analysis	13
An inverse potential problem for fractional subdiffusion: local stability analysis and coupled complex boundary method	13
Stability analysis for Caputo fractional-order discrete system with first-order operator	13
Radial symmetry and Liouville theorem for master equations	13
The well-posedness analysis in Besov-type spaces for multi-term time-fractional wave equations	13
Infinitely many sign-changing solutions for a kind of fractional Klein-Gordon-Maxwell system	13
Initial-boundary value problems for coupled systems of time-fractional diffusion equations	13
Controllability of Hilfer fractional backward evolution systems	13
Fractional Wiener chaos: Part 1	13
The fractional stochastic heat equation driven by time-space white noise	12
Fractional models for analysis of economic risks	12
Generalized fractional derivatives generated by Dickman subordinator and related stochastic processes	12
Fractional boundary value problems and elastic sticky brownian motions	12
Properties of the 1st-level general fractional derivatives with arbitrary order on a finite interval	11
Complete synchronization of discrete-time fractional-order neural networks with leakage and distributed delays	11
On the properties of the Le Roy function and of its generalized forms	11
Polynomial decay of porous elastic system with fractional damping	11
Asymptotic behaviors for distribution dependent stochastic partial differential equations driven by fractional Brownian motion	11
A unified analysis framework for generalized fractional Moore–Gibson–Thompson equations: Well-posedness and singular limits	11
Limitations and applications in a fractional Barbalat’s Lemma	10
Stability analysis for nonlocal initial value problems involving nonlocal Caputo derivative and loss-of-regularity nonlinearities	10
Young type inequality and Hausdorff–Young type inequality for convolution operator associated with fractional Fourier transform of $$\alpha $$-order	10
Analysis of a fractional viscoelastic Euler-Bernoulli beam and identification of its piecewise continuous polynomial order	10
On the multivariate generalized counting process and its time-changed variants	10
Boundedness of fractional integrals on special John–Nirenberg–Campanato and Hardy-type spaces via congruent cubes	10
Superlinear solutions of sublinear fractional differential equations and regular variation	10
A high order predictor-corrector method with non-uniform meshes for fractional differential equations	10
A unified way to solve IVPs and IBVPs for the time-fractional diffusion-wave equation	10
On solutions of space-time fractional nonlinear Fokker–Planck equation. II	10
Fractional Toeplitz operators with radial symbols	9
Bifurcations of a fractional-order neutral-type neural network	9
Fractional-order problem coupled with a second-order Moreau’s sweeping process	9
A critical elliptic problem involving exponential and singular nonlinearities	9
Berry-Esséen bounds for the statistical estimators of an Ornstein-Uhlenbeck process driven by a general Gaussian noise	9
Fractional Musielak-Sobolev spaces: study of generalized double phase problem with Choquard-logarithmic nonlinearity	9
Controllability and observability of linear time-varying fractional systems	9
Global solutions to semilinear subdiffusion-normal transport equations: well-posedness and Strichartz estimates	9
Log-concavity and log-convexity of series containing multiple Pochhammer symbols	9
Application of seventh-kind Chebyshev polynomials to variable-order reaction-diffusion and advection-dispersion equations	9
Concave-convex critical problems for the spectral fractional laplacian with mixed boundary conditions	8
Approximate solutions for fractional stochastic integro-differential equation with short memory driven by non-instantaneous impulses	8

Convergence to logarithmic-type functions of solutions of fractional systems with Caputo-Hadamard and Hadamard fractional derivatives	8
Some results concerning B-local variable Morrey-Lorentz spaces	8
Nonlocal Kirchhoff-type problems with singular nonlinearity: existence, uniqueness and bifurcation	8
Correction: Existence, uniqueness and regularity for a semilinear stochastic subdiffusion with integrated multiplicative noise	8
On the asymptotic behaviour of the Fourier transform of the Mittag-Leffler function	8
On the existence and uniqueness of the solution to multifractional stochastic delay differential equation	8
Exact controllability for nonlinear Hilfer fractional Volterra-Fredholm integrodifferential equations $$(1< \varrho < 2)$$ with infinite delay based on the measure of noncompactness	8
Abstract fractional linear pseudo-parabolic equations in Banach spaces: well-posedness, regularity, and asymptotic behavior	8
Separation method of semi-fixed variables for solving a generalized time-fractional reaction-diffusion equation	8
Existence, comparison, and monotonicity of principal eigenvalues of fractional Sturm-Liouville problems involving Riemann-Liouville derivatives	8
Asymptotics and geometric flows for a class of nonlocal curvatures	8
Boundedness of the fractional maximal operator on Orlicz-Lorentz spaces	8
Multiplicity of solutions for a fractional Kirchhoff type equation with a critical nonlocal term	8
Solving 3D fractional Schrödinger systems on the basis of Phragmén–Lindelöf methods	7
A tempered subdiffusive Black–Scholes model	7
An efficient numerical method to the stochastic fractional heat equation with random coefficients and fractionally integrated multiplicative noise	7
Monotonicity and uniqueness of positive solutions to elliptic fractional p-equations	7
Existence, nonexistence and multiplicity of bounded solutions to a nonlinear BVP associated to the fractional Laplacian	7
Solutions of time fractional anomalous diffusion equations with coefficients depending on both time and space variables	7
A parallel multi-domain spectral collocation algorithm for the Caputo-Hadamard type time fractional differential equation	7
Study on the diffusion fractional m-Laplacian with singular potential term	7
On a new class of segmental type periodic/anti-periodic fractional boundary value problems	7
The sliding method for fractional Laplacian systems	7
Fractional coupled Halanay inequality and its applications	7
Multiplicity of solutions for mixed local-nonlocal elliptic equations with singular nonlinearity	7
Schrödinger-Maxwell equations driven by mixed local-nonlocal operators	7
Space–time duality for fractional powers of sectorial operators, with applications to graph laplacians	7
Positive controllability and positive output controllability of fractional discrete linear time-invariant systems	7
Landweber iteration method for simultaneous inversion of the source term and initial value of the Rayleigh-Stokes equation	7
A Robust fractional order PI controller for time constant variations	7
Continuous-time MISO fractional system identification using higher-order-statistics	7
The nonlinear fractional Rayleigh-Stokes problem on an infinite interval	7
A fast fractional block-centered finite difference method for two-sided space-fractional diffusion equations on general nonuniform grids	7
Fractional 3D Diffraction Optics: Resolvent Function Solution of Cauchy Problem	7
Existence and asymptotic behavior of normalized ground state solutions to fractional Schrödinger equation with singular potential and Hartree-type nonlinearity	7
A semilinear diffusion PDE with variable order time-fractional Caputo derivative subject to homogeneous Dirichlet boundary conditions	7
Sensitivity analysis for optimal control problems governed by Hilfer fractional differential hemivariational inequalities	7
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
A simple series representation for a class of fractal interpolation functions	6
Wellposedness of the recovery of multi-factor source in fractional diffusion equations by integral type observation	6
Reachability of time-varying fractional dynamical systems with Riemann-Liouville fractional derivative	6
Finding extrema using the unified fractional derivative: a conjecture	6
Subordination and memory dependent kinetics in diffusion and relaxation phenomena	6
Halanay inequality involving $$\psi -$$Caputo derivative and application to a neural network system	6
Game-theoretical problems for fractional-order nonstationary systems	6
A fractional version of the recursive Tau method for solving a general class of Abel-Volterra integral equations systems	6
A second-order fitted scheme for time fractional telegraph equations involving weak singularity	6
A class of positive Fox H-functions	6
Existence and asymptotic behavior of square-mean S-asymptotically periodic solutions for fractional stochastic evolution equation with delay	6
Identifying source term and initial value simultaneously for the time-fractional diffusion equation with Caputo-like hyper-Bessel operator	6
Non-stationary zipper $$\alpha $$-fractal functions and associated fractal operator	6
S-asymptotically $$\omega $$-periodic solutions for time-space fractional nonlocal reaction-diffusion equation with superlinear growth nonlinear terms	6
On self-adjoint Caputo-type fractional Hahn difference equations	6
Existence and uniqueness of a weak solution to fractional single-phase-lag heat equation	6
On the three dimensional generalized Navier-Stokes equations with damping	6
Appell system associated with the infinite dimensional Fractional Pascal measure	6
Pullback dynamics of 2D non-autonomous Reissner-Mindlin-Timoshenko plate systems	6
Dependence of solutions on the order of the Caputo-Hadamard derivative and illustrative examples	6
The existence and averaging principle for Caputo fractional stochastic delay differential systems	6
Unification of popular artificial neural network activation functions	6
Operational matrix based numerical scheme for the solution of time fractional diffusion equations	6
Cauchy problem for non-autonomous fractional evolution equations	5
Mixed fractional stochastic heat equation with additive fractional-colored noise	5
Shock models driven by a bivariate mixture tempered space fractional Poisson process	5
A time-space fractional parabolic type problem: weak, strong and classical solutions	5
An alternative definition of the fractional in space derivatives	5
On multiterm time-fractional diffusion equations with additional memory	5
Invariant tori for the fractional nonlinear Schrödinger equation with nonlinearity periodically depending on spatial variable	5
Lie symmetry analysis of two–dimensional fractional integro–differential equations	5
Strong stationarity for non-smooth control problems with fractional semi-linear elliptic equations in dimension $$N\le 3$$	5
Discrete-time general fractional calculus	5
On the existence of solutions for a class of nonlinear fractional Schrödinger-Poisson system: Subcritical and critical cases	5
Persistence and asymptotic behavior of classical solutions to a parabolic-parabolic chemotaxis model with a mixed operator and logistic source on $${\mathbb {R}}^N$$	5
Sticky Brownian motions on star graphs	5
Hopf’s lemma and radial symmetry for the Logarithmic Laplacian problem	5
Fractional Derivatives: the ultimate operator for modelling complex viscoelastic materials?	5
Adaptive finite-time fuzzy composite control for nonlinear fractional-order systems based on complexity avoidance	5
Global optimization of a nonlinear system of differential equations involving $$\psi $$-Hilfer fractional derivatives of complex order	5
Pricing European option under the generalized fractional jump-diffusion model	5

Generalized fractional operators do not preserve periodicity	5
A Fractional-Order Commensurate and Incommensurate Study on Predator-Prey System with Allee in Predator and Fear Effect	5
Multiplicity of couple solution for a fractional $$(\varphi , \psi )$$-like system	5
Collage theorems, invertibility and fractal functions	5
On approximate controllability of semi-linear neutral integro-differential evolution systems with state-dependent nonlocal conditions	5
A mutually exciting rough jump-diffusion for financial modelling	5
Spectral analysis of a family of nonsymmetric fractional elliptic operators	5
High-order fractional spectral collocation method for the nonsmooth solutions of nonlinear right-sided Caputo terminal value problems	5
Existence, multiplicity and asymptotic behaviour of normalized solutions to non-autonomous fractional HLS lower critical Choquard equation	5
Analytical closed-form solution of the Bagley-Torvik equation	5
Fractional calculus modifications to the kinetic equations of statistical mechanics	4
A class of Hilfer fractional differential evolution hemivariational inequalities with history-dependent operators	4
Abstract fractional inverse source problem of order $$0<\alpha <1$$ in a Banach space	4
Existence and multiplicity of positive solutions for a critical fractional Laplacian equation with singular nonlinearity	4
Rich phenomenology of the solutions in a fractional Duffing equation	4
Positive solutions for fractional-order boundary value problems with or without dependence of integer-order ones	4
Comparison principles for the time-fractional diffusion equations with the Robin boundary conditions. Part I: Linear equations	4
Localized special John–Nirenberg–Campanato spaces via congruent cubes with applications to boundedness of local Calderón–Zygmund singular integrals and fractional integrals	4
Fractional differential equation on the whole axis involving Liouville derivative	4
Fractional Fokker-Planck-Kolmogorov equations with Hölder continuous drift	4
Uncertain differential equations driven by fractional Liu process	4
A bifurcation result for a Keller-Segel-type problem	4
Existence of periodic mild solutions for fractional impulsive evolution equation with piecewise Caputo derivative and delay	4
Asymptotics of the s-fractional Gaussian perimeter as $$s\rightarrow 0^+$$	4
Energy stability and convergence of variable-step L1 scheme for the time fractional Swift-Hohenberg model	4
Variable-order fractional 1-Laplacian diffusion equations for multiplicative noise removal	4
Two-dimensional space-fractional transient groundwater flow equation with nonlinear head-dependent recharge and extraction source	4
A new approach to multi-delay matrix valued fractional linear differential equations with constant coefficients	4
On the computation of the Mittag-Leffler function of fractional powers of accretive operators	4
Sum of series and new relations for Mittag-Leffler functions	4
Space-time fractional parabolic equations on a metric star graph with spatial fractional derivative of Sturm-Liouville type: analysis and discretization	4
A variational theory for integral functionals involving finite-horizon fractional gradients	4
Barenblatt solutions for the time-fractional porous medium equation: approach via integral equations	4
Correction: Comparison principles for the time-fractional diffusion equations with the Robin boundary conditions. Part I: Linear equations	4
Representations of abstract resolvent families on time scales via Laplace Transform	4
Principal curves to fractional m-Laplacian systems and related maximum and comparison principles	4
Multivariable functions represented as fractional power series and generalized Taylor’s formula	3
Impulse response of commensurate fractional-order systems: multiple complex poles	3
Existence and uniqueness of discrete weighted pseudo S-asymptotically $$\omega $$-periodic solution to abstract semilinear superdiffusive difference equation	3
On the kinetics of $$\psi $$-fractional differential equations	3
Mixed order elliptic problems driven by a singularity, a Choquard type term and a discontinuous power nonlinearity with critical variable exponents	3
Multivariate Generalized Fractional Integrals from a Statistical Point of View	3
Applications of Babenko’s method to a class of integral equations	3
Fractional differential equations via Fourier transform and curvilinear cuts in the complex plane	3
Topological effects on the multiplicity of positive solutions to a fractional upper critical choquard equation	3
$$\psi $$-Hilfer type linear fractional differential equations with variable coefficients	3
Existence and multiplicity of solutions to magnetic Kirchhoff equations in Orlicz-Sobolev spaces	3
Global solvability of inverse coefficient problem for one fractional diffusion equation with initial non-local and integral overdetermination conditions	3
Variational methods for nonpositive mixed local–nonlocal operators	3
The impact of Richardson extrapolation on the asymptotic global error estimation of uniform $$\text {L2-1}_\sigma $$ scheme for subdiffusion equation with multiple delays	3
Generalized fractional Dirac type operators	3
An elementary inequality for dissipative Caputo fractional differential equations	3
Topological properties of solution sets for control problems driven by fractional delay differential quasi-hemivariational inequalities and applications	3
Asymptotical stabilization of fuzzy semilinear dynamic systems involving the generalized Caputo fractional derivative for $$q \in (1,2)$$	3
Continuous dependence and h-Mittag-Leffler-Ulam’s type stability for semilinear fractional integro-differential equations in fractional power spaces	3
Solvability for a class of two-term nonlinear functional boundary value problems and its applications	3
Pointwise characterizations of variable Besov and Triebel-Lizorkin spaces via Hajłasz gradients	3
Focusing on the constraint minimizers of the almost mass critical fractional NLS equations	3
Ground state solution for the Choquard equation under the superposition of operators of mixed fractional order	3
Bifurcation results and multiple solutions for the fractional (p, q)-Laplace operators	3
Analysis and computation for quenching solution to the time-space fractional Kawarada problem	3
Analysis of a class of completely non-local elliptic diffusion operators	3
Existence and Controllability Results for Hilfer Fractional Evolution Equations via Integral Contractors	3
Homogenization and inverse problems for fractional diffusion equations	3
No-regret and low-regret controls of space-time fractional parabolic Sturm-Liouville equations in a star graph	3
Nonlinear iterated function systems and fractal interpolation functions with Pata-type contractions	3
Simulating neuronal dynamics in fractional adaptive exponential integrate-and-fire models	3
Fractional order control for unstable first order processes with time delays	3
Non-homogeneous generalized fractional skellam process	3
Queuing models with Mittag-Leffler inter-event times	3
An anomalous fractional diffusion operator	3
Characteristics of Riemann-Liouville fractional integral of hidden variable fractal interpolation function constructed using Rakotch contractive mappings	3
On some even-sequential fractional boundary-value problems	3
Multi-parametric Le Roy function	3
Skellam and time-changed variants of the generalized fractional counting process	3
Topological properties of the solution set for Caputo fractional evolution inclusions involving delay	3
Asymptotic synchronization for Riemann-Liouville fractional-order delayed BAM neural networks by the exponential-type controllers	3
The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces II	3
Reconstruction of a fractional evolution equation with a source	3
Subordination principle and Feynman-Kac formulae for generalized time-fractional evolution equations	3
Attractors of Caputo semi-dynamical systems	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
Monotone iterative technique for multi-term time fractional measure differential equations	2
Remarks on the nonlinear fractional Choquard equation	2
Multiple solutions for anisotropic nonlocal problems with variable exponents	2
Measure attractors of asymptotic autonomy fractional stochastic reaction-diffusion equations on unbounded domains	2
On the variable order fractional calculus of fractal interpolation functions	2
On a class of time-space fractional nonlinear Schrödinger equation with the Riesz potential or Bessel potential	2
Initial-boundary value problems for multi-term time-fractional wave equations	2
Limiting behavior of invariant measures for stochastic fractional Ginzburg-Landau equations on unbounded domains	2
Ground states for p-fractional Choquard-type equations with doubly or triply critical nonlinearity	2
Existence of positive solutions for fractional delayed evolution equations of order $$\gamma \in (1,2)$$ via measure of non-compactness	2
An improved fractional predictor-corrector method for nonlinear fractional differential equations with initial singularity	2
Pricing Vulnerable Options in Fractional Brownian Markets: a Partial Differential Equations Approach	2