Fractional Calculus and Applied Analysis

Article	Citations
Sonine-Dimovski transform and spectral synthesis associated with the hyper-Bessel operator on the complex plane	50
On generalized K-functionals in $$L_p$$ for $$0<p<1$$	41
Symmetry of solutions for asymptotically symmetric nonlocal parabolic equations	40
Asymptotically autonomous dynamics for fractional subcritical nonclassical diffusion equations driven by nonlinear colored noise	36
Rigidity of phase transitions for the fractional elliptic Gross-Pitaevskii system	33
Considerations regarding the accuracy of fractional numerical computations	32
Differential transforms related to Caputo time-fractional derivatives and semigroups generated by fractional Schrödinger operators	31
Stochastic heat equation driven by space-only fractional Lévy noise	29
Fractional differential equations of Bagley-Torvik and Langevin type	27
The Spatially Variant Fractional Laplacian	27
On heat equations associated with fractional harmonic oscillators	26
Box dimension of mixed Katugampola fractional integral of two-dimensional continuous functions	26
Bernstein Fractional Derivatives: Censoring and Stochastic Processes	25
Blow-up for a non-linear stable non-Gaussian process in fractional time	25
Discrete fractional distributed Halanay inequality and applications in discrete fractional order neural network systems	22
Analysis of BURA and BURA-based approximations of fractional powers of sparse SPD matrices	22
A review of constitutive models for non-Newtonian fluids	21
Mixed slow-fast stochastic differential equations: Averaging principle result	21
Stability analysis of Hilfer fractional stochastic switched dynamical systems with non-Gaussian process and impulsive effects	21
Fractional differential operators, fractional Sobolev spaces and fractional variation on homogeneous Carnot groups	20
Dual Spaces of Anisotropic Variable Hardy–Lorentz Spaces and Their Applications	19
On approximate controllability of multi-term time fractional measure differential equations with nonlocal conditions	18
Representations of solutions of systems of time-fractional pseudo-differential equations	17
Differentiation of integral Mittag-Leffler and integral Wright functions with respect to parameters	17
Abstract multi-term fractional difference equations	16

Multi-term fractional oscillation integro-differential equations	16
Multi-parametric Le Roy function revisited	15
A Fractional Order Derivative Newton-Raphson Method for the Computation of the Power Flow Problem Solution in Energy Systems	15
Radial symmetry and Hopf lemma for fully nonlinear parabolic equations involving the fractional Laplacian	14
Asymptotic analysis of three-parameter Mittag-Leffler function with large parameters, and application to sub-diffusion equation involving Bessel operator	14
Direct and inverse abstract Cauchy problems with fractional powers of almost sectorial operators	14
Fractal Riemann-Stieltjes Calculus	14
An inverse potential problem for fractional subdiffusion: local stability analysis and coupled complex boundary method	13
On the convergence of the Galerkin method for random fractional differential equations	13
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
Concentration phenomenon of solutions for fractional Choquard equations with upper critical growth	13
Two disjoint and infinite sets of solutions for a concave-convex critical fractional Laplacian equation	13
Complete synchronization of discrete-time fractional-order neural networks with leakage and distributed delays	13
Decay estimates and extinction properties for some parabolic equations with fractional time derivatives	13
The well-posedness analysis in Besov-type spaces for multi-term time-fractional wave equations	12
A high order predictor-corrector method with non-uniform meshes for fractional differential equations	12
Radial symmetry and Liouville theorem for master equations	12
Limitations and applications in a fractional Barbalat’s Lemma	12
Infinitely many sign-changing solutions for a kind of fractional Klein-Gordon-Maxwell system	12
Stability analysis for Caputo fractional-order discrete system with first-order operator	12
A unified analysis framework for generalized fractional Moore–Gibson–Thompson equations: Well-posedness and singular limits	12
Generalized fractional derivatives generated by Dickman subordinator and related stochastic processes	12
Fractional Wiener chaos: Part 1	12
On the properties of the Le Roy function and of its generalized forms	12
The fractional stochastic heat equation driven by time-space white noise	12
Initial-boundary value problems for coupled systems of time-fractional diffusion equations	12
Fractional models for analysis of economic risks	11
Controllability of Hilfer fractional backward evolution systems	11
Riemann-Liouville derivatives of abstract functions and Sobolev spaces	11
Asymptotic behaviors for distribution dependent stochastic partial differential equations driven by fractional Brownian motion	11
A unified way to solve IVPs and IBVPs for the time-fractional diffusion-wave equation	11
Fractional boundary value problems and elastic sticky brownian motions	11
A critical elliptic problem involving exponential and singular nonlinearities	10
Berry-Esséen bounds for the statistical estimators of an Ornstein-Uhlenbeck process driven by a general Gaussian noise	10
Weighted estimates for operators of fractional integration of variable order in generalized variable Hölder spaces	10
On the multivariate generalized counting process and its time-changed variants	10
Application of seventh-kind Chebyshev polynomials to variable-order reaction-diffusion and advection-dispersion equations	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
Concave-convex critical problems for the spectral fractional laplacian with mixed boundary conditions	9
Controllability and observability of linear time-varying fractional systems	9
Fractional-order problem coupled with a second-order Moreau’s sweeping process	9
Stability analysis for nonlocal initial value problems involving nonlocal Caputo derivative and loss-of-regularity nonlinearities	9
Log-concavity and log-convexity of series containing multiple Pochhammer symbols	9
Analysis of a fractional viscoelastic Euler-Bernoulli beam and identification of its piecewise continuous polynomial order	9
Fractional Musielak-Sobolev spaces: study of generalized double phase problem with Choquard-logarithmic nonlinearity	8
Abstract fractional linear pseudo-parabolic equations in Banach spaces: well-posedness, regularity, and asymptotic behavior	8
On the existence and uniqueness of the solution to multifractional stochastic delay differential equation	8
Some results concerning B-local variable Morrey-Lorentz spaces	8
Nonlocal Kirchhoff-type problems with singular nonlinearity: existence, uniqueness and bifurcation	8

Some nonexistence results for space–time fractional Schrödinger equations without gauge invariance	8
On the asymptotic behaviour of the Fourier transform of the Mittag-Leffler function	8
Vallée-Poussin theorem for fractional functional differential equations	8
Asymptotics and geometric flows for a class of nonlocal curvatures	8
Exact controllability for nonlinear Hilfer fractional Volterra-Fredholm integrodifferential equations $$(1< \varrho < 2)$$ with infinite delay based on the measure of noncompactness	8
A Robust fractional order PI controller for time constant variations	8
Convergence to logarithmic-type functions of solutions of fractional systems with Caputo-Hadamard and Hadamard fractional derivatives	8
Approximate solutions for fractional stochastic integro-differential equation with short memory driven by non-instantaneous impulses	8
Existence, comparison, and monotonicity of principal eigenvalues of fractional Sturm-Liouville problems involving Riemann-Liouville derivatives	8
Stability and stabilization of short memory fractional differential equations with delayed impulses	8
Correction: Existence, uniqueness and regularity for a semilinear stochastic subdiffusion with integrated multiplicative noise	8
Multiplicity of solutions for a fractional Kirchhoff type equation with a critical nonlocal term	8
A semilinear diffusion PDE with variable order time-fractional Caputo derivative subject to homogeneous Dirichlet boundary conditions	8
Existence and asymptotic behavior of normalized ground state solutions to fractional Schrödinger equation with singular potential and Hartree-type nonlinearity	7
The sliding method for fractional Laplacian systems	7
On a new class of segmental type periodic/anti-periodic fractional boundary value problems	7
Existence and uniqueness of a weak solution to fractional single-phase-lag heat equation	7
A simple series representation for a class of fractal interpolation functions	7
Anisotropic variable Campanato-type spaces and their Carleson measure characterizations	7
Continuous-time MISO fractional system identification using higher-order-statistics	7
The nonlinear fractional Rayleigh-Stokes problem on an infinite interval	7
Landweber iteration method for simultaneous inversion of the source term and initial value of the Rayleigh-Stokes equation	7
Fractional coupled Halanay inequality and its applications	7
A fast fractional block-centered finite difference method for two-sided space-fractional diffusion equations on general nonuniform grids	7
Operational matrix based numerical scheme for the solution of time fractional diffusion equations	7
Schrödinger-Maxwell equations driven by mixed local-nonlocal operators	7
An efficient numerical method to the stochastic fractional heat equation with random coefficients and fractionally integrated multiplicative noise	7
A parallel multi-domain spectral collocation algorithm for the Caputo-Hadamard type time fractional differential equation	7
Solving 3D fractional Schrödinger systems on the basis of Phragmén–Lindelöf methods	7
Sensitivity analysis for optimal control problems governed by Hilfer fractional differential hemivariational inequalities	7
Study on the diffusion fractional m-Laplacian with singular potential term	7
Special solutions to the space fractional diffusion problem	7
Existence, nonexistence and multiplicity of bounded solutions to a nonlinear BVP associated to the fractional Laplacian	7
Fractional 3D Diffraction Optics: Resolvent Function Solution of Cauchy Problem	7
Monotonicity and uniqueness of positive solutions to elliptic fractional p-equations	7
A tempered subdiffusive Black–Scholes model	7
Numerical scheme for Erdélyi–Kober fractional diffusion equation using Galerkin–Hermite method	7
Unification of popular artificial neural network activation functions	6
S-asymptotically $$\omega $$-periodic solutions for time-space fractional nonlocal reaction-diffusion equation with superlinear growth nonlinear terms	6
A second-order fitted scheme for time fractional telegraph equations involving weak singularity	6
An inverse problem of determining the fractional order in the TFDE using the measurement at one space-time point	6
Identifying source term and initial value simultaneously for the time-fractional diffusion equation with Caputo-like hyper-Bessel operator	6
A mutually exciting rough jump-diffusion for financial modelling	6
A class of positive Fox H-functions	6
On approximate controllability of semi-linear neutral integro-differential evolution systems with state-dependent nonlocal conditions	6
Existence and asymptotic behavior of square-mean S-asymptotically periodic solutions for fractional stochastic evolution equation with delay	6
Reachability of time-varying fractional dynamical systems with Riemann-Liouville fractional derivative	6
Halanay inequality involving $$\psi -$$Caputo derivative and application to a neural network system	6
Appell system associated with the infinite dimensional Fractional Pascal measure	6
A fractional version of the recursive Tau method for solving a general class of Abel-Volterra integral equations systems	6
On the three dimensional generalized Navier-Stokes equations with damping	6
Hopf’s lemma and radial symmetry for the Logarithmic Laplacian problem	6
Persistence and asymptotic behavior of classical solutions to a parabolic-parabolic chemotaxis model with a mixed operator and logistic source on $${\mathbb {R}}^N$$	6
A time-space fractional parabolic type problem: weak, strong and classical solutions	6
Non-stationary zipper $$\alpha $$-fractal functions and associated fractal operator	6
Pullback dynamics of 2D non-autonomous Reissner-Mindlin-Timoshenko plate systems	6
On self-adjoint Caputo-type fractional Hahn difference equations	6
Game-theoretical problems for fractional-order nonstationary systems	6
Dependence of solutions on the order of the Caputo-Hadamard derivative and illustrative examples	6
Finding extrema using the unified fractional derivative: a conjecture	6
Sticky Brownian motions on star graphs	6
The existence and averaging principle for Caputo fractional stochastic delay differential systems	6
Shock models driven by a bivariate mixture tempered space fractional Poisson process	6
Wellposedness of the recovery of multi-factor source in fractional diffusion equations by integral type observation	6
Subordination and memory dependent kinetics in diffusion and relaxation phenomena	6
Analytical closed-form solution of the Bagley-Torvik equation	5
Adaptive finite-time fuzzy composite control for nonlinear fractional-order systems based on complexity avoidance	5
Collage theorems, invertibility and fractal functions	5
Fractional Derivatives: the ultimate operator for modelling complex viscoelastic materials?	5
Strong stationarity for non-smooth control problems with fractional semi-linear elliptic equations in dimension $$N\le 3$$	5
Asymptotics of the s-fractional Gaussian perimeter as $$s\rightarrow 0^+$$	5
On the computation of the Mittag-Leffler function of fractional powers of accretive operators	5
Existence and multiplicity of positive solutions for a critical fractional Laplacian equation with singular nonlinearity	5
Pricing European option under the generalized fractional jump-diffusion model	5
On multiterm time-fractional diffusion equations with additional memory	5
Cauchy problem for non-autonomous fractional evolution equations	5
Multiplicity of couple solution for a fractional $$(\varphi , \psi )$$-like system	5
Generalized fractional operators do not preserve periodicity	5
A variational theory for integral functionals involving finite-horizon fractional gradients	5
Sum of series and new relations for Mittag-Leffler functions	5

Spectral analysis of a family of nonsymmetric fractional elliptic operators	5
A bifurcation result for a Keller-Segel-type problem	5
Discrete-time general fractional calculus	5
Global optimization of a nonlinear system of differential equations involving $$\psi $$-Hilfer fractional derivatives of complex order	5
Mixed fractional stochastic heat equation with additive fractional-colored noise	5
A Fractional-Order Commensurate and Incommensurate Study on Predator-Prey System with Allee in Predator and Fear Effect	5
On the existence of solutions for a class of nonlinear fractional Schrödinger-Poisson system: Subcritical and critical cases	5
High-order fractional spectral collocation method for the nonsmooth solutions of nonlinear right-sided Caputo terminal value problems	5
Space-time fractional parabolic equations on a metric star graph with spatial fractional derivative of Sturm-Liouville type: analysis and discretization	5
Existence, multiplicity and asymptotic behaviour of normalized solutions to non-autonomous fractional HLS lower critical Choquard equation	5
Invariant tori for the fractional nonlinear Schrödinger equation with nonlinearity periodically depending on spatial variable	5
Queuing models with Mittag-Leffler inter-event times	4
A class of Hilfer fractional differential evolution hemivariational inequalities with history-dependent operators	4
Barenblatt solutions for the time-fractional porous medium equation: approach via integral equations	4
Comparison principles for the time-fractional diffusion equations with the Robin boundary conditions. Part I: Linear equations	4
On the kinetics of $$\psi $$-fractional differential equations	4
Positive solutions for fractional-order boundary value problems with or without dependence of integer-order ones	4
A new approach to multi-delay matrix valued fractional linear differential equations with constant coefficients	4
Asymptotical stabilization of fuzzy semilinear dynamic systems involving the generalized Caputo fractional derivative for $$q \in (1,2)$$	4
Existence of periodic mild solutions for fractional impulsive evolution equation with piecewise Caputo derivative and delay	4
Multivariate Generalized Fractional Integrals from a Statistical Point of View	4
Principal curves to fractional m-Laplacian systems and related maximum and comparison principles	4
Fractional Euler numbers and generalized proportional fractional logistic differential equation	4
Abstract fractional inverse source problem of order $$0<\alpha <1$$ in a Banach space	4
Representations of abstract resolvent families on time scales via Laplace Transform	4
Impulse response of commensurate fractional-order systems: multiple complex poles	4
Solvability for a class of two-term nonlinear functional boundary value problems and its applications	4
Localized special John–Nirenberg–Campanato spaces via congruent cubes with applications to boundedness of local Calderón–Zygmund singular integrals and fractional integrals	4
Applications of Babenko’s method to a class of integral equations	4
Global solutions of nonlinear fractional diffusion equations with time-singular sources and perturbed orders	4
Homogenization and inverse problems for fractional diffusion equations	4
Fractional differential equation on the whole axis involving Liouville derivative	4
Focusing on the constraint minimizers of the almost mass critical fractional NLS equations	4
Fractional Fokker-Planck-Kolmogorov equations with Hölder continuous drift	4
Correction: Comparison principles for the time-fractional diffusion equations with the Robin boundary conditions. Part I: Linear equations	4
Mixed order elliptic problems driven by a singularity, a Choquard type term and a discontinuous power nonlinearity with critical variable exponents	4
Skellam and time-changed variants of the generalized fractional counting process	4
Energy stability and convergence of variable-step L1 scheme for the time fractional Swift-Hohenberg model	4
On some even-sequential fractional boundary-value problems	4
Variable-order fractional 1-Laplacian diffusion equations for multiplicative noise removal	4
An anomalous fractional diffusion operator	4
Fractional calculus modifications to the kinetic equations of statistical mechanics	4
Pointwise characterizations of variable Besov and Triebel-Lizorkin spaces via Hajłasz gradients	4
Rich phenomenology of the solutions in a fractional Duffing equation	4
Fractional scalar products as probes of chaos and fractal dimension	3
Discrete fractional-order Halanay inequality with mixed time delays and applications in discrete fractional-order neural network systems	3
Characteristics of Riemann-Liouville fractional integral of hidden variable fractal interpolation function constructed using Rakotch contractive mappings	3
Properties of the multi-index special function $${\mathcal {W}}^{\left( \bar{\alpha },\bar{\nu }\right) }(z)$$	3
Subordination principle and Feynman-Kac formulae for generalized time-fractional evolution equations	3
Numerical investigation of two models of nonlinear fractional reaction subdiffusion equations	3
Existence and multiplicity of solutions to magnetic Kirchhoff equations in Orlicz-Sobolev spaces	3
Topological properties of the solution set for Caputo fractional evolution inclusions involving delay	3
Ground state solution for the Choquard equation under the superposition of operators of mixed fractional order	3
Analysis of a class of completely non-local elliptic diffusion operators	3
Wright functions of the second kind and Whittaker functions	3
Simulating neuronal dynamics in fractional adaptive exponential integrate-and-fire models	3
Nonlinear iterated function systems and fractal interpolation functions with Pata-type contractions	3
An elementary inequality for dissipative Caputo fractional differential equations	3
Multi-parametric Le Roy function	3
No-regret and low-regret controls of space-time fractional parabolic Sturm-Liouville equations in a star graph	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
Optimal regional control for a class of semilinear time-fractional diffusion systems with distributed feedback	3
Existence and uniqueness of discrete weighted pseudo S-asymptotically $$\omega $$-periodic solution to abstract semilinear superdiffusive difference equation	3
A Meyer-Itô formula for stable processes via fractional calculus	3
The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces II	3
Hardy–Hénon fractional equation with nonlinearities involving exponential critical growth	3
Bifurcation results and multiple solutions for the fractional (p, q)-Laplace operators	3
$$\psi $$-Hilfer type linear fractional differential equations with variable coefficients	3
Global solvability of inverse coefficient problem for one fractional diffusion equation with initial non-local and integral overdetermination conditions	3
Existence and Controllability Results for Hilfer Fractional Evolution Equations via Integral Contractors	3
Non-homogeneous generalized fractional skellam process	3
Optimized fractional-order Butterworth filter design in complex F-plane	3
Attractors of Caputo semi-dynamical systems	3
Fractional order control for unstable first order processes with time delays	3
Generalized fractional Dirac type operators	3
On the well-posedness of a nonlocal kinetic model for dilute polymers with anomalous diffusion	3
Existence, uniqueness and regularity for a semilinear stochastic subdiffusion with integrated multiplicative noise	3
Fractional differential equations via Fourier transform and curvilinear cuts in the complex plane	3
Existence and regularity of mild solutions to backward problem for nonlinear fractional super-diffusion equations in Banach spaces	3
Fractional integral operators on Orlicz slice Hardy spaces	3
Relative controllability of linear state-delay fractional systems	3
On discrete tempered fractional calculus and its application	3
Decay solutions to abstract impulsive fractional mobile–immobile equations involving superlinear nonlinearities	3
Continuous dependence and h-Mittag-Leffler-Ulam’s type stability for semilinear fractional integro-differential equations in fractional power spaces	3
Analysis and computation for quenching solution to the time-space fractional Kawarada problem	3
Topological properties of solution sets for control problems driven by fractional delay differential quasi-hemivariational inequalities and applications	3
Variational methods for nonpositive mixed local–nonlocal operators	3
Reconstruction of a fractional evolution equation with a source	3
A spectral approach to non-linear weakly singular fractional integro-differential equations	3
On the Filippov-Ważewski relaxation theorem for a certain class of fractional differential inclusions	3
Author Correction: On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications	3