Fractional Calculus and Applied Analysis

Article	Citations
Sonine-Dimovski transform and spectral synthesis associated with the hyper-Bessel operator on the complex plane	44
Bounds for mixing times for finite semi-Markov processes with heavy-tail jump distribution	44
Blow-up for a non-linear stable non-Gaussian process in fractional time	33
On generalized K-functionals in $$L_p$$ for $$0<p<1$$	32
Symmetry of solutions for asymptotically symmetric nonlocal parabolic equations	32
Box dimension of mixed Katugampola fractional integral of two-dimensional continuous functions	29
Rigidity of phase transitions for the fractional elliptic Gross-Pitaevskii system	29
Considerations regarding the accuracy of fractional numerical computations	28
Differential transforms related to Caputo time-fractional derivatives and semigroups generated by fractional Schrödinger operators	27
Stability analysis of Hilfer fractional stochastic switched dynamical systems with non-Gaussian process and impulsive effects	27
The Spatially Variant Fractional Laplacian	25
Stochastic heat equation driven by space-only fractional Lévy noise	25
Bernstein Fractional Derivatives: Censoring and Stochastic Processes	24
Asymptotically autonomous dynamics for fractional subcritical nonclassical diffusion equations driven by nonlinear colored noise	24
A review of constitutive models for non-Newtonian fluids	23
Fractional differential equations of Bagley-Torvik and Langevin type	20
On heat equations associated with fractional harmonic oscillators	20
Analysis of BURA and BURA-based approximations of fractional powers of sparse SPD matrices	20
Discrete fractional distributed Halanay inequality and applications in discrete fractional order neural network systems	20
Fractional differential operators, fractional Sobolev spaces and fractional variation on homogeneous Carnot groups	19
A Fractional Order Derivative Newton-Raphson Method for the Computation of the Power Flow Problem Solution in Energy Systems	19
Dual Spaces of Anisotropic Variable Hardy–Lorentz Spaces and Their Applications	18
Mixed slow-fast stochastic differential equations: Averaging principle result	18
Abstract multi-term fractional difference equations	17
Asymptotic analysis of three-parameter Mittag-Leffler function with large parameters, and application to sub-diffusion equation involving Bessel operator	16

On approximate controllability of multi-term time fractional measure differential equations with nonlocal conditions	16
Multi-parametric Le Roy function revisited	16
Delsarte equation for Caputo operator of fractional calculus	16
Differentiation of integral Mittag-Leffler and integral Wright functions with respect to parameters	15
Representations of solutions of systems of time-fractional pseudo-differential equations	15
Radial symmetry and Hopf lemma for fully nonlinear parabolic equations involving the fractional Laplacian	14
Multi-term fractional oscillation integro-differential equations	14
Concentration phenomenon of solutions for fractional Choquard equations with upper critical growth	13
Decay estimates and extinction properties for some parabolic equations with fractional time derivatives	13
Two disjoint and infinite sets of solutions for a concave-convex critical fractional Laplacian equation	13
Stability analysis for Caputo fractional-order discrete system with first-order operator	12
On the properties of the Le Roy function and of its generalized forms	12
On the convergence of the Galerkin method for random fractional differential equations	12
Fractional Wiener chaos: Part 1	12
Complete synchronization of discrete-time fractional-order neural networks with leakage and distributed delays	12
The well-posedness analysis in Besov-type spaces for multi-term time-fractional wave equations	12
An inverse potential problem for fractional subdiffusion: local stability analysis and coupled complex boundary method	11
Radial symmetry and Liouville theorem for master equations	11
A unified analysis framework for generalized fractional Moore–Gibson–Thompson equations: Well-posedness and singular limits	11
A high order predictor-corrector method with non-uniform meshes for fractional differential equations	11
Infinitely many sign-changing solutions for a kind of fractional Klein-Gordon-Maxwell system	11
Initial-boundary value problems for coupled systems of time-fractional diffusion equations	11
Controllability of Hilfer fractional backward evolution systems	11
Limitations and applications in a fractional Barbalat’s Lemma	11
Fractional boundary value problems and elastic sticky brownian motions	11
Generalized fractional derivatives generated by Dickman subordinator and related stochastic processes	11
Fractional models for analysis of economic risks	10
A critical elliptic problem involving exponential and singular nonlinearities	10
A unified way to solve IVPs and IBVPs for the time-fractional diffusion-wave equation	10
Riemann-Liouville derivatives of abstract functions and Sobolev spaces	10
Weighted estimates for operators of fractional integration of variable order in generalized variable Hölder spaces	10
The fractional stochastic heat equation driven by time-space white noise	10
Berry-Esséen bounds for the statistical estimators of an Ornstein-Uhlenbeck process driven by a general Gaussian noise	10
Boundedness of fractional integrals on special John–Nirenberg–Campanato and Hardy-type spaces via congruent cubes	10
Analysis of a fractional viscoelastic Euler-Bernoulli beam and identification of its piecewise continuous polynomial order	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
Controllability and observability of linear time-varying fractional systems	9
Superlinear solutions of sublinear fractional differential equations and regular variation	9
Correction: Existence, uniqueness and regularity for a semilinear stochastic subdiffusion with integrated multiplicative noise	9
On the multivariate generalized counting process and its time-changed variants	9
Fractional-order problem coupled with a second-order Moreau’s sweeping process	9
Integral operators defined “up to a polynomial”	9
Convergence to logarithmic-type functions of solutions of fractional systems with Caputo-Hadamard and Hadamard fractional derivatives	8
Concave-convex critical problems for the spectral fractional laplacian with mixed boundary conditions	8
From time to times	8
Sequential generalized Riemann–Liouville derivatives based on distributional convolution	8
Some nonexistence results for space–time fractional Schrödinger equations without gauge invariance	8
Sensitivity analysis for optimal control problems governed by Hilfer fractional differential hemivariational inequalities	8
Approximate solutions for fractional stochastic integro-differential equation with short memory driven by non-instantaneous impulses	8

Abstract fractional linear pseudo-parabolic equations in Banach spaces: well-posedness, regularity, and asymptotic behavior	8
On the asymptotic behaviour of the Fourier transform of the Mittag-Leffler function	8
Stability and stabilization of short memory fractional differential equations with delayed impulses	8
Multiplicity of solutions for a fractional Kirchhoff type equation with a critical nonlocal term	8
Numerical scheme for Erdélyi–Kober fractional diffusion equation using Galerkin–Hermite method	8
Landweber iteration method for simultaneous inversion of the source term and initial value of the Rayleigh-Stokes equation	8
Vallée-Poussin theorem for fractional functional differential equations	8
Convolution series and the generalized convolution Taylor formula	8
Fractional Musielak-Sobolev spaces: study of generalized double phase problem with Choquard-logarithmic nonlinearity	8
Study on the diffusion fractional m-Laplacian with singular potential term	8
Nonlocal Kirchhoff-type problems with singular nonlinearity: existence, uniqueness and bifurcation	8
A semilinear diffusion PDE with variable order time-fractional Caputo derivative subject to homogeneous Dirichlet boundary conditions	8
On the existence and uniqueness of the solution to multifractional stochastic delay differential equation	8
The nonlinear fractional Rayleigh-Stokes problem on an infinite interval	7
Continuous-time MISO fractional system identification using higher-order-statistics	7
Solving 3D fractional Schrödinger systems on the basis of Phragmén–Lindelöf methods	7
An inverse problem of determining the fractional order in the TFDE using the measurement at one space-time point	7
A fractional version of the recursive Tau method for solving a general class of Abel-Volterra integral equations systems	7
Appell system associated with the infinite dimensional Fractional Pascal measure	7
Schrödinger-Maxwell equations driven by mixed local-nonlocal operators	7
A fast fractional block-centered finite difference method for two-sided space-fractional diffusion equations on general nonuniform grids	7
Fractional boundary value problems	7
Anisotropic variable Campanato-type spaces and their Carleson measure characterizations	7
Monotonicity and uniqueness of positive solutions to elliptic fractional p-equations	7
Infinitely many large solutions to a variable order nonlocal singular equation	7
S-asymptotically $$\omega $$-periodic solutions for time-space fractional nonlocal reaction-diffusion equation with superlinear growth nonlinear terms	7
Existence and uniqueness of a weak solution to fractional single-phase-lag heat equation	7
An efficient numerical method to the stochastic fractional heat equation with random coefficients and fractionally integrated multiplicative noise	7
The sliding method for fractional Laplacian systems	7
On a new class of segmental type periodic/anti-periodic fractional boundary value problems	7
A tempered subdiffusive Black–Scholes model	7
On the three dimensional generalized Navier-Stokes equations with damping	7
A second-order fitted scheme for time fractional telegraph equations involving weak singularity	7
Monte Carlo method for fractional-order differentiation	7
Special solutions to the space fractional diffusion problem	6
Fractional 3D Diffraction Optics: Resolvent Function Solution of Cauchy Problem	6
Operational matrix based numerical scheme for the solution of time fractional diffusion equations	6
Identifying source term and initial value simultaneously for the time-fractional diffusion equation with Caputo-like hyper-Bessel operator	6
Existence and asymptotic behavior of square-mean S-asymptotically periodic solutions for fractional stochastic evolution equation with delay	6
Hopf’s lemma and radial symmetry for the Logarithmic Laplacian problem	6
A simple series representation for a class of fractal interpolation functions	6
Game-theoretical problems for fractional-order nonstationary systems	6
Unification of popular artificial neural network activation functions	6
On approximate controllability of semi-linear neutral integro-differential evolution systems with state-dependent nonlocal conditions	6
Dependence of solutions on the order of the Caputo-Hadamard derivative and illustrative examples	6
Subordination and memory dependent kinetics in diffusion and relaxation phenomena	6
Pullback dynamics of 2D non-autonomous Reissner-Mindlin-Timoshenko plate systems	6
Halanay inequality involving $$\psi -$$Caputo derivative and application to a neural network system	6
Existence, nonexistence and multiplicity of bounded solutions to a nonlinear BVP associated to the fractional Laplacian	6
Hölder regularity for the nonlinear stochastic time-fractional slow & fast diffusion equations on $${\mathbb {R}}^d$$	6
Non-stationary zipper $$\alpha $$-fractal functions and associated fractal operator	6
Finding extrema using the unified fractional derivative: a conjecture	6
The existence and averaging principle for Caputo fractional stochastic delay differential systems	6
Adaptive finite-time fuzzy composite control for nonlinear fractional-order systems based on complexity avoidance	5
Invariant tori for the fractional nonlinear Schrödinger equation with nonlinearity periodically depending on spatial variable	5
Pricing European option under the generalized fractional jump-diffusion model	5
High-order fractional spectral collocation method for the nonsmooth solutions of nonlinear right-sided Caputo terminal value problems	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
Multiplicity of couple solution for a fractional $$(\varphi , \psi )$$-like system	5
Mixed fractional stochastic heat equation with additive fractional-colored noise	5
Reachability of time-varying fractional dynamical systems with Riemann-Liouville fractional derivative	5
Discrete-time general fractional calculus	5
Existence and multiplicity of positive solutions for a critical fractional Laplacian equation with singular nonlinearity	5
Generalized fractional operators do not preserve periodicity	5
Existence, multiplicity and asymptotic behaviour of normalized solutions to non-autonomous fractional HLS lower critical Choquard equation	5
Strong stationarity for non-smooth control problems with fractional semi-linear elliptic equations in dimension $$N\le 3$$	5
On the existence of solutions for a class of nonlinear fractional Schrödinger-Poisson system: Subcritical and critical cases	5
Cauchy problem for non-autonomous fractional evolution equations	5
A time-space fractional parabolic type problem: weak, strong and classical solutions	5
A mutually exciting rough jump-diffusion for financial modelling	5
Global optimization of a nonlinear system of differential equations involving $$\psi $$-Hilfer fractional derivatives of complex order	5
A bifurcation result for a Keller-Segel-type problem	5
Spectral analysis of a family of nonsymmetric fractional elliptic operators	5
Attractors of Caputo fractional differential equations with triangular vector fields	5
Fractional Derivatives: the ultimate operator for modelling complex viscoelastic materials?	5
The fractional variation and the precise representative of $$BV^{\alpha ,p}$$ functions	5
Collage theorems, invertibility and fractal functions	5
Sticky Brownian motions on star graphs	5
The Cauchy problem and distribution of local fluctuations of one Riesz gravitational field	5
An anomalous fractional diffusion operator	4

Solvability for a class of two-term nonlinear functional boundary value problems and its applications	4
Mixed order elliptic problems driven by a singularity, a Choquard type term and a discontinuous power nonlinearity with critical variable exponents	4
An elementary inequality for dissipative Caputo fractional differential equations	4
Asymptotic cycles in fractional maps of arbitrary positive orders	4
Energy stability and convergence of variable-step L1 scheme for the time fractional Swift-Hohenberg model	4
Global solutions of nonlinear fractional diffusion equations with time-singular sources and perturbed orders	4
Rich phenomenology of the solutions in a fractional Duffing equation	4
A variational theory for integral functionals involving finite-horizon fractional gradients	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
Sum of series and new relations for Mittag-Leffler functions	4
Queuing models with Mittag-Leffler inter-event times	4
Asymptotical stabilization of fuzzy semilinear dynamic systems involving the generalized Caputo fractional derivative for $$q \in (1,2)$$	4
Homogenization and inverse problems for fractional diffusion equations	4
Comparison principles for the time-fractional diffusion equations with the Robin boundary conditions. Part I: Linear equations	4
Skellam and time-changed variants of the generalized fractional counting process	4
Representations of abstract resolvent families on time scales via Laplace Transform	4
Analytical solutions for fractional partial delay differential-algebraic equations with Dirichlet boundary conditions defined on a finite domain	4
Pointwise characterizations of variable Besov and Triebel-Lizorkin spaces via Hajłasz gradients	4
Fractional Fokker-Planck-Kolmogorov equations with Hölder continuous drift	4
On the computation of the Mittag-Leffler function of fractional powers of accretive operators	4
Space-time fractional parabolic equations on a metric star graph with spatial fractional derivative of Sturm-Liouville type: analysis and discretization	4
A new approach to multi-delay matrix valued fractional linear differential equations with constant coefficients	4
Variable-order fractional 1-Laplacian diffusion equations for multiplicative noise removal	4
Global solvability of inverse coefficient problem for one fractional diffusion equation with initial non-local and integral overdetermination conditions	4
Fractional Euler numbers and generalized proportional fractional logistic differential equation	4
On the fractional Laplacian of variable order	4
On some even-sequential fractional boundary-value problems	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
Principal curves to fractional m-Laplacian systems and related maximum and comparison principles	4
Asymptotics of the s-fractional Gaussian perimeter as $$s\rightarrow 0^+$$	4
Correction: Comparison principles for the time-fractional diffusion equations with the Robin boundary conditions. Part I: Linear equations	4
Simulating neuronal dynamics in fractional adaptive exponential integrate-and-fire models	3
Analysis and computation for quenching solution to the time-space fractional Kawarada problem	3
Variational methods for nonpositive mixed local–nonlocal 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
Existence and uniqueness of discrete weighted pseudo S-asymptotically $$\omega $$-periodic solution to abstract semilinear superdiffusive difference equation	3
Existence and Controllability Results for Hilfer Fractional Evolution Equations via Integral Contractors	3
Reconstruction of a fractional evolution equation with a source	3
Fractional integral operators on Orlicz slice Hardy spaces	3
Attractors of Caputo semi-dynamical systems	3
Impulse response of commensurate fractional-order systems: multiple complex poles	3
Wright functions of the second kind and Whittaker functions	3
Existence and multiplicity of solutions to magnetic Kirchhoff equations in Orlicz-Sobolev spaces	3
On discrete tempered fractional calculus and its application	3
An inverse problem of determining orders of systems of fractional pseudo-differential equations	3
Topological properties of the solution set for Caputo fractional evolution inclusions involving delay	3
Non-homogeneous generalized fractional skellam process	3
No-regret and low-regret controls of space-time fractional parabolic Sturm-Liouville equations in a star graph	3
On the Filippov-Ważewski relaxation theorem for a certain class of fractional differential inclusions	3
Multi-parametric Le Roy function	3
A higher order resolvent-positive finite difference approximation for fractional derivatives on bounded domains	3
Nonlinear iterated function systems and fractal interpolation functions with Pata-type contractions	3
A spectral approach to non-linear weakly singular fractional integro-differential equations	3
Applications of Babenko’s method to a class of integral equations	3
Characteristics of Riemann-Liouville fractional integral of hidden variable fractal interpolation function constructed using Rakotch contractive mappings	3
The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces II	3
$$\psi $$-Hilfer type linear fractional differential equations with variable coefficients	3
Subordination principle and Feynman-Kac formulae for generalized time-fractional evolution equations	3
A Meyer-Itô formula for stable processes via fractional calculus	3
Computation of the inverse Mittag–Leffler function and its application to modeling ultraslow dynamics	3
Optimized fractional-order Butterworth filter design in complex F-plane	3
Analysis of a class of completely non-local elliptic diffusion operators	3
Topological properties of solution sets for control problems driven by fractional delay differential quasi-hemivariational inequalities and applications	3
Fractional vector-valued nonuniform MRA and associated wavelet packets on $$L^2\big ({\mathbb {R}},{\mathbb {C}}^M\big )$$	3
Fractional order control for unstable first order processes with time delays	3
On the kinetics of $$\psi $$-fractional differential equations	3
Fractional differential equations via Fourier transform and curvilinear cuts in the complex plane	3
Generalized fractional Dirac type operators	3
Hardy–Hénon fractional equation with nonlinearities involving exponential critical growth	3
Multiple solutions for anisotropic nonlocal problems with variable exponents	2
On a class of time-space fractional nonlinear Schrödinger equation with the Riesz potential or Bessel potential	2
Lump solutions of the fractional Kadomtsev–Petviashvili equation	2
Fractional Sobolev type spaces of functions of two variables via Riemann-Liouville derivatives	2
Least energy sign-changing solutions for fractional critical Kirchhoff–Schrödinger–Poisson with steep potential well	2
Final value problem for Rayleigh-Stokes type equations involving weak-valued nonlinearities	2
Weighted boundedness of fractional integrals associated with admissible functions on spaces of homogeneous type	2
Remarks on the nonlinear fractional Choquard equation	2
Initial-boundary value problems for multi-term time-fractional wave equations	2
On the variable order fractional calculus of fractal interpolation functions	2
Limiting behavior of invariant measures for stochastic fractional Ginzburg-Landau equations on unbounded domains	2
Multiplicity of solutions for fractional Hamiltonian systems with combined nonlinearities and without coercive conditions	2
On variable-order fractional linear viscoelasticity	2
Inverse coefficient problems for the heat equation with fractional Laplacian	2
The overdamped generalized Langevin equation with Hermite noise	2
RETRACTED ARTICLE: Averaging principle for stochastic Caputo fractional differential equations with non-Lipschitz condition	2
Measure attractors of asymptotic autonomy fractional stochastic reaction-diffusion equations on unbounded domains	2
Pricing Vulnerable Options in Fractional Brownian Markets: a Partial Differential Equations Approach	2
Dynamical repulsive fractional potential fields in 3D environment	2
Some boundedness results for Riemann-Liouville tempered fractional integrals	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 mild solutions of the generalized nonlinear fractional pseudo-parabolic equation with a nonlocal condition	2
Two families of second-order fractional numerical formulas and applications to fractional differential equations	2
An improved fractional predictor-corrector method for nonlinear fractional differential equations with initial singularity	2