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 $$0<p<1$$	42
Symmetry of solutions for asymptotically symmetric nonlocal parabolic equations	41
Asymptotically autonomous dynamics for fractional subcritical nonclassical diffusion equations driven by nonlinear colored noise	38
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	29
Stochastic heat equation driven by space-only fractional Lévy noise	28
Box dimension of mixed Katugampola fractional integral of two-dimensional continuous functions	27
The Spatially Variant Fractional Laplacian	27
Discrete fractional distributed Halanay inequality and applications in discrete fractional order neural network systems	26
Bernstein Fractional Derivatives: Censoring and Stochastic Processes	26
Blow-up for a non-linear stable non-Gaussian process in fractional time	26
On heat equations associated with fractional harmonic oscillators	22
A review of constitutive models for non-Newtonian fluids	22
Stability analysis of Hilfer fractional stochastic switched dynamical systems with non-Gaussian process and impulsive effects	21
Analysis of BURA and BURA-based approximations of fractional powers of sparse SPD matrices	21
Fractional differential equations of Bagley-Torvik and Langevin type	21
Mixed slow-fast stochastic differential equations: Averaging principle result	19
Dual Spaces of Anisotropic Variable Hardy–Lorentz Spaces and Their Applications	18
Fractional differential operators, fractional Sobolev spaces and fractional variation on homogeneous Carnot groups	18
On approximate controllability of multi-term time fractional measure differential equations with nonlocal conditions	17
Representations of solutions of systems of time-fractional pseudo-differential equations	16
Direct and inverse abstract Cauchy problems with fractional powers of almost sectorial operators	16
Differentiation of integral Mittag-Leffler and integral Wright functions with respect to parameters	16

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

Abstract fractional linear pseudo-parabolic equations in Banach spaces: well-posedness, regularity, and asymptotic behavior	8
A semilinear diffusion PDE with variable order time-fractional Caputo derivative subject to homogeneous Dirichlet boundary conditions	8
Vallée-Poussin theorem for fractional functional differential equations	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
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
Some nonexistence results for space–time fractional Schrödinger equations without gauge invariance	8
On the existence and uniqueness of the solution to multifractional stochastic delay differential equation	8
Convergence to logarithmic-type functions of solutions of fractional systems with Caputo-Hadamard and Hadamard fractional derivatives	8
Exact controllability for nonlinear Hilfer fractional Volterra-Fredholm integrodifferential equations $$(1< \varrho < 2)$$ with infinite delay based on the measure of noncompactness	8
Nonlocal Kirchhoff-type problems with singular nonlinearity: existence, uniqueness and bifurcation	8
Existence and asymptotic behavior of normalized ground state solutions to fractional Schrödinger equation with singular potential and Hartree-type nonlinearity	8
Continuous-time MISO fractional system identification using higher-order-statistics	7
A parallel multi-domain spectral collocation algorithm for the Caputo-Hadamard type time fractional differential equation	7
Numerical scheme for Erdélyi–Kober fractional diffusion equation using Galerkin–Hermite method	7
A Robust fractional order PI controller for time constant variations	7
Monotonicity and uniqueness of positive solutions to elliptic fractional p-equations	7
A fast fractional block-centered finite difference method for two-sided space-fractional diffusion equations on general nonuniform grids	7
A simple series representation for a class of fractal interpolation functions	7
Anisotropic variable Campanato-type spaces and their Carleson measure characterizations	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
The sliding method for fractional Laplacian systems	7
Fractional coupled Halanay inequality and its applications	7
Fractional 3D Diffraction Optics: Resolvent Function Solution of Cauchy Problem	7
A fractional version of the recursive Tau method for solving a general class of Abel-Volterra integral equations systems	7
Multiplicity of solutions for mixed local-nonlocal elliptic equations with singular nonlinearity	7
On a new class of segmental type periodic/anti-periodic fractional boundary value problems	7
A tempered subdiffusive Black–Scholes model	7
Positive controllability and positive output controllability of fractional discrete linear time-invariant systems	7
Study on the diffusion fractional m-Laplacian with singular potential term	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
Special solutions to the space fractional diffusion problem	7
Appell system associated with the infinite dimensional Fractional Pascal measure	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
Existence, nonexistence and multiplicity of bounded solutions to a nonlinear BVP associated to the fractional Laplacian	6
An inverse problem of determining the fractional order in the TFDE using the measurement at one space-time point	6
Game-theoretical problems for fractional-order nonstationary systems	6
A second-order fitted scheme for time fractional telegraph equations involving weak singularity	6
Pullback dynamics of 2D non-autonomous Reissner-Mindlin-Timoshenko plate systems	6
Shock models driven by a bivariate mixture tempered space fractional Poisson process	6
Hopf’s lemma and radial symmetry for the Logarithmic Laplacian problem	6
The existence and averaging principle for Caputo fractional stochastic delay differential systems	6
On the three dimensional generalized Navier-Stokes equations with damping	6
Unification of popular artificial neural network activation functions	6
On self-adjoint Caputo-type fractional Hahn difference equations	6
A class of positive Fox H-functions	6
Reachability of time-varying fractional dynamical systems with Riemann-Liouville fractional derivative	6
Existence and asymptotic behavior of square-mean S-asymptotically periodic solutions for fractional stochastic evolution equation with delay	6
Wellposedness of the recovery of multi-factor source in fractional diffusion equations by integral type observation	6
Halanay inequality involving $$\psi -$$Caputo derivative and application to a neural network system	6
S-asymptotically $$\omega $$-periodic solutions for time-space fractional nonlocal reaction-diffusion equation with superlinear growth nonlinear terms	6
Operational matrix based numerical scheme for the solution of time fractional diffusion equations	6
Existence and uniqueness of a weak solution to fractional single-phase-lag heat equation	6
Finding extrema using the unified fractional derivative: a conjecture	6
Subordination and memory dependent kinetics in diffusion and relaxation phenomena	6
Dependence of solutions on the order of the Caputo-Hadamard derivative and illustrative examples	6
Non-stationary zipper $$\alpha $$-fractal functions and associated fractal operator	6
A variational theory for integral functionals involving finite-horizon fractional gradients	5
Strong stationarity for non-smooth control problems with fractional semi-linear elliptic equations in dimension $$N\le 3$$	5
High-order fractional spectral collocation method for the nonsmooth solutions of nonlinear right-sided Caputo terminal value problems	5
Adaptive finite-time fuzzy composite control for nonlinear fractional-order systems based on complexity avoidance	5
A Fractional-Order Commensurate and Incommensurate Study on Predator-Prey System with Allee in Predator and Fear Effect	5
Identifying source term and initial value simultaneously for the time-fractional diffusion equation with Caputo-like hyper-Bessel operator	5
Collage theorems, invertibility and fractal functions	5
On the existence of solutions for a class of nonlinear fractional Schrödinger-Poisson system: Subcritical and critical cases	5
Existence, multiplicity and asymptotic behaviour of normalized solutions to non-autonomous fractional HLS lower critical Choquard equation	5
Space-time fractional parabolic equations on a metric star graph with spatial fractional derivative of Sturm-Liouville type: analysis and discretization	5
Invariant tori for the fractional nonlinear Schrödinger equation with nonlinearity periodically depending on spatial variable	5
Analytical closed-form solution of the Bagley-Torvik equation	5
Pricing European option under the generalized fractional jump-diffusion model	5
A mutually exciting rough jump-diffusion for financial modelling	5
Fractional Derivatives: the ultimate operator for modelling complex viscoelastic materials?	5
Multiplicity of couple solution for a fractional $$(\varphi , \psi )$$-like system	5
A time-space fractional parabolic type problem: weak, strong and classical solutions	5
Global optimization of a nonlinear system of differential equations involving $$\psi $$-Hilfer fractional derivatives of complex order	5

Generalized fractional operators do not preserve periodicity	5
On the computation of the Mittag-Leffler function of fractional powers of accretive operators	5
Spectral analysis of a family of nonsymmetric fractional elliptic operators	5
On multiterm time-fractional diffusion equations with additional memory	5
Mixed fractional stochastic heat equation with additive fractional-colored noise	5
Cauchy problem for non-autonomous fractional evolution equations	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
On approximate controllability of semi-linear neutral integro-differential evolution systems with state-dependent nonlocal conditions	5
Discrete-time general fractional calculus	5
Abstract fractional inverse source problem of order $$0<\alpha <1$$ in a Banach space	5
Existence and multiplicity of positive solutions for a critical fractional Laplacian equation with singular nonlinearity	4
Variable-order fractional 1-Laplacian diffusion equations for multiplicative noise removal	4
Skellam and time-changed variants of the generalized fractional counting process	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
Localized special John–Nirenberg–Campanato spaces via congruent cubes with applications to boundedness of local Calderón–Zygmund singular integrals and fractional integrals	4
Fractional calculus modifications to the kinetic equations of statistical mechanics	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
Uncertain differential equations driven by fractional Liu process	4
Global solutions of nonlinear fractional diffusion equations with time-singular sources and perturbed orders	4
Multivariate Generalized Fractional Integrals from a Statistical Point of View	4
A new approach to multi-delay matrix valued fractional linear differential equations with constant coefficients	4
Representations of abstract resolvent families on time scales via Laplace Transform	4
Energy stability and convergence of variable-step L1 scheme for the time fractional Swift-Hohenberg model	4
Queuing models with Mittag-Leffler inter-event times	4
Existence of periodic mild solutions for fractional impulsive evolution equation with piecewise Caputo derivative and delay	4
Barenblatt solutions for the time-fractional porous medium equation: approach via integral equations	4
Fractional Fokker-Planck-Kolmogorov equations with Hölder continuous drift	4
Asymptotics of the s-fractional Gaussian perimeter as $$s\rightarrow 0^+$$	4
Principal curves to fractional m-Laplacian systems and related maximum and comparison principles	4
An anomalous fractional diffusion operator	4
Focusing on the constraint minimizers of the almost mass critical fractional NLS equations	4
Mixed order elliptic problems driven by a singularity, a Choquard type term and a discontinuous power nonlinearity with critical variable exponents	4
On some even-sequential fractional boundary-value problems	4
Correction: Comparison principles for the time-fractional diffusion equations with the Robin boundary conditions. Part I: Linear equations	4
Positive solutions for fractional-order boundary value problems with or without dependence of integer-order ones	4
Rich phenomenology of the solutions in a fractional Duffing equation	4
Sum of series and new relations for Mittag-Leffler functions	4
A bifurcation result for a Keller-Segel-type problem	4
Optimal regional control for a class of semilinear time-fractional diffusion systems with distributed feedback	3
Decay solutions to abstract impulsive fractional mobile–immobile equations involving superlinear nonlinearities	3
Multi-parametric Le Roy function	3
Existence and multiplicity of solutions to magnetic Kirchhoff equations in Orlicz-Sobolev spaces	3
Multivariable functions represented as fractional power series and generalized Taylor’s formula	3
Existence and regularity of mild solutions to backward problem for nonlinear fractional super-diffusion equations in Banach spaces	3
Reconstruction of a fractional evolution equation with a source	3
Existence and Controllability Results for Hilfer Fractional Evolution Equations via Integral Contractors	3
Applications of Babenko’s method to a class of integral equations	3
No-regret and low-regret controls of space-time fractional parabolic Sturm-Liouville equations in a star graph	3
Fractional order control for unstable first order processes with time delays	3
Analysis and computation for quenching solution to the time-space fractional Kawarada problem	3
Global solvability of inverse coefficient problem for one fractional diffusion equation with initial non-local and integral overdetermination conditions	3
Solvability for a class of two-term nonlinear functional boundary value problems and its applications	3
Continuous dependence and h-Mittag-Leffler-Ulam’s type stability for semilinear fractional integro-differential equations in fractional power spaces	3
Discrete fractional-order Halanay inequality with mixed time delays and applications in discrete fractional-order neural network systems	3
On discrete tempered fractional calculus and its application	3
Non-homogeneous generalized fractional skellam process	3
Hardy–Hénon fractional equation with nonlinearities involving exponential critical growth	3
Ground state solution for the Choquard equation under the superposition of operators of mixed fractional order	3
Variational methods for nonpositive mixed local–nonlocal operators	3
Characteristics of Riemann-Liouville fractional integral of hidden variable fractal interpolation function constructed using Rakotch contractive mappings	3
$$\psi $$-Hilfer type linear fractional differential equations with variable coefficients	3
Fractional differential equations via Fourier transform and curvilinear cuts in the complex plane	3
Analysis of a class of completely non-local elliptic diffusion operators	3
A spectral approach to non-linear weakly singular fractional integro-differential equations	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
Impulse response of commensurate fractional-order systems: multiple complex poles	3
Asymptotical stabilization of fuzzy semilinear dynamic systems involving the generalized Caputo fractional derivative for $$q \in (1,2)$$	3
Subordination principle and Feynman-Kac formulae for generalized time-fractional evolution equations	3
Generalized fractional Dirac type operators	3
Time optimal controls for Hilfer fractional evolution equations	3
A Meyer-Itô formula for stable processes via fractional calculus	3
Topological properties of solution sets for control problems driven by fractional delay differential quasi-hemivariational inequalities and applications	3
Topological effects on the multiplicity of positive solutions to a fractional upper critical choquard equation	3
Bifurcation results and multiple solutions for the fractional (p, q)-Laplace operators	3
Simulating neuronal dynamics in fractional adaptive exponential integrate-and-fire models	3
Existence and uniqueness of discrete weighted pseudo S-asymptotically $$\omega $$-periodic solution to abstract semilinear superdiffusive difference equation	3
Optimized fractional-order Butterworth filter design in complex F-plane	3
Attractors of Caputo semi-dynamical systems	3
Topological properties of the solution set for Caputo fractional evolution inclusions involving delay	3
An elementary inequality for dissipative Caputo fractional differential equations	3
On the Filippov-Ważewski relaxation theorem for a certain class of fractional differential inclusions	3
Homogenization and inverse problems for fractional diffusion equations	3
On the kinetics of $$\psi $$-fractional differential equations	3
Nonlinear iterated function systems and fractal interpolation functions with Pata-type contractions	3
The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces II	3
Lump solutions of the fractional Kadomtsev–Petviashvili equation	2
Ground state solution for a generalized Choquard Schr$$\ddot{\text {o}}$$dinger equation with vanishing potential in homogeneous fractional Musielak Sobolev spaces	2
On the variable order fractional calculus of fractal interpolation functions	2
Pricing Vulnerable Options in Fractional Brownian Markets: a Partial Differential Equations Approach	2
Multiple solutions for anisotropic nonlocal problems with variable exponents	2
Limiting behavior of invariant measures for stochastic fractional Ginzburg-Landau equations on unbounded domains	2
An improved fractional predictor-corrector method for nonlinear fractional differential equations with initial singularity	2