Fractional Calculus and Applied Analysis

Article	Citations
Sonine-Dimovski transform and spectral synthesis associated with the hyper-Bessel operator on the complex plane	43
Bounds for mixing times for finite semi-Markov processes with heavy-tail jump distribution	41
Blow-up for a non-linear stable non-Gaussian process in fractional time	33
Analysis of BURA and BURA-based approximations of fractional powers of sparse SPD matrices	32
On generalized K-functionals in $$L_p$$ for $$0<p<1$$	30
Symmetry of solutions for asymptotically symmetric nonlocal parabolic equations	28
Stability analysis of Hilfer fractional stochastic switched dynamical systems with non-Gaussian process and impulsive effects	27
Considerations regarding the accuracy of fractional numerical computations	27
Discrete fractional distributed Halanay inequality and applications in discrete fractional order neural network systems	25
Box dimension of mixed Katugampola fractional integral of two-dimensional continuous functions	25
The Spatially Variant Fractional Laplacian	24
Differential transforms related to Caputo time-fractional derivatives and semigroups generated by fractional Schrödinger operators	24
Stochastic heat equation driven by space-only fractional Lévy noise	24
On heat equations associated with fractional harmonic oscillators	23
Asymptotically autonomous dynamics for fractional subcritical nonclassical diffusion equations driven by nonlinear colored noise	20
A review of constitutive models for non-Newtonian fluids	20
Rigidity of phase transitions for the fractional elliptic Gross-Pitaevskii system	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
Fractional differential equations of Bagley-Torvik and Langevin type	19
Dual Spaces of Anisotropic Variable Hardy–Lorentz Spaces and Their Applications	18
Delsarte equation for Caputo operator of fractional calculus	17
Mixed slow-fast stochastic differential equations: Averaging principle result	17
Abstract multi-term fractional difference equations	17
On approximate controllability of multi-term time fractional measure differential equations with nonlocal conditions	16

Multi-parametric Le Roy function revisited	16
Asymptotic analysis of three-parameter Mittag-Leffler function with large parameters, and application to sub-diffusion equation involving Bessel operator	16
Multi-term fractional oscillation integro-differential equations	16
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
Two disjoint and infinite sets of solutions for a concave-convex critical fractional Laplacian equation	14
Differentiation of integral Mittag-Leffler and integral Wright functions with respect to parameters	14
Concentration phenomenon of solutions for fractional Choquard equations with upper critical growth	14
Infinitely many sign-changing solutions for a kind of fractional Klein-Gordon-Maxwell system	13
Decay estimates and extinction properties for some parabolic equations with fractional time derivatives	13
On the convergence of the Galerkin method for random fractional differential equations	12
Controllability of Hilfer fractional backward evolution systems	12
The fractional stochastic heat equation driven by time-space white noise	12
Complete synchronization of discrete-time fractional-order neural networks with leakage and distributed delays	12
Generalized fractional derivatives generated by Dickman subordinator and related stochastic processes	12
A unified analysis framework for generalized fractional Moore–Gibson–Thompson equations: Well-posedness and singular limits	11
Fractional boundary value problems and elastic sticky brownian motions	11
Fractional models for analysis of economic risks	11
Initial-boundary value problems for coupled systems of time-fractional diffusion equations	11
On the properties of the Le Roy function and of its generalized forms	11
The well-posedness analysis in Besov-type spaces for multi-term time-fractional wave equations	10
Limitations and applications in a fractional Barbalat’s Lemma	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	10
Stability analysis for Caputo fractional-order discrete system with first-order operator	10
Fractional Wiener chaos: Part 1	10
On the multivariate generalized counting process and its time-changed variants	10
A critical elliptic problem involving exponential and singular nonlinearities	10
Radial symmetry and Liouville theorem for master equations	10
A high order predictor-corrector method with non-uniform meshes for fractional differential equations	10
Riemann-Liouville derivatives of abstract functions and Sobolev spaces	10
Superlinear solutions of sublinear fractional differential equations and regular variation	10
From time to times	9
Integral operators defined “up to a polynomial”	9
Controllability and observability of linear time-varying fractional systems	9
Log-concavity and log-convexity of series containing multiple Pochhammer symbols	9
Weighted estimates for operators of fractional integration of variable order in generalized variable Hölder spaces	9
Berry-Esséen bounds for the statistical estimators of an Ornstein-Uhlenbeck process driven by a general Gaussian noise	9
Fractional-order problem coupled with a second-order Moreau’s sweeping process	9
Analysis of a fractional viscoelastic Euler-Bernoulli beam and identification of its piecewise continuous polynomial order	9
Correction: Existence, uniqueness and regularity for a semilinear stochastic subdiffusion with integrated multiplicative noise	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
Convolution series and the generalized convolution Taylor formula	8
Multiplicity of solutions for a fractional Kirchhoff type equation with a critical nonlocal term	8
Stability and stabilization of short memory fractional differential equations with delayed impulses	8
Concave-convex critical problems for the spectral fractional laplacian with mixed boundary conditions	8
Convergence to logarithmic-type functions of solutions of fractional systems with Caputo-Hadamard and Hadamard fractional derivatives	8
A Strong Maximum Principle for the Fractional Laplace Equation with Mixed Boundary Condition	8
Sequential generalized Riemann–Liouville derivatives based on distributional convolution	8

Nonlocal Kirchhoff-type problems with singular nonlinearity: existence, uniqueness and bifurcation	8
Approximate solutions for fractional stochastic integro-differential equation with short memory driven by non-instantaneous impulses	8
Fractional Musielak-Sobolev spaces: study of generalized double phase problem with Choquard-logarithmic nonlinearity	8
Vallée-Poussin theorem for fractional functional differential equations	8
Explicit Representation of Discrete Fractional Resolvent Families in Banach Spaces	8
Some nonexistence results for space–time fractional Schrödinger equations without gauge invariance	8
Study on the diffusion fractional m-Laplacian with singular potential term	8
Monte Carlo method for fractional-order differentiation	7
Solving 3D fractional Schrödinger systems on the basis of Phragmén–Lindelöf methods	7
Schrödinger-Maxwell equations driven by mixed local-nonlocal operators	7
Convergence Rate Estimates for the Kernelized Predictor Corrector Method for Fractional Order Initial Value Problems	7
Anisotropic variable Campanato-type spaces and their Carleson measure characterizations	7
A tempered subdiffusive Black–Scholes model	7
The nonlinear fractional Rayleigh-Stokes problem on an infinite interval	7
B-Spline Collocation Discretizations of Caputo and Riemann-Liouville Derivatives: A Matrix Comparison	7
The sliding method for fractional Laplacian systems	7
Fractional boundary value problems	7
A semilinear diffusion PDE with variable order time-fractional Caputo derivative subject to homogeneous Dirichlet boundary conditions	7
Continuous-time MISO fractional system identification using higher-order-statistics	7
Numerical scheme for Erdélyi–Kober fractional diffusion equation using Galerkin–Hermite method	7
Infinitely many large solutions to a variable order nonlocal singular equation	7
On a new class of segmental type periodic/anti-periodic fractional boundary value problems	7
An efficient numerical method to the stochastic fractional heat equation with random coefficients and fractionally integrated multiplicative noise	7
Landweber iteration method for simultaneous inversion of the source term and initial value of the Rayleigh-Stokes equation	7
Sensitivity analysis for optimal control problems governed by Hilfer fractional differential hemivariational inequalities	7
A fast fractional block-centered finite difference method for two-sided space-fractional diffusion equations on general nonuniform grids	7
Monotonicity and uniqueness of positive solutions to elliptic fractional p-equations	7
Operational matrix based numerical scheme for the solution of time fractional diffusion equations	7
Subordination and memory dependent kinetics in diffusion and relaxation phenomena	6
Existence and asymptotic behavior of square-mean S-asymptotically periodic solutions for fractional stochastic evolution equation with delay	6
A second-order fitted scheme for time fractional telegraph equations involving weak singularity	6
S-asymptotically $$\omega $$-periodic solutions for time-space fractional nonlocal reaction-diffusion equation with superlinear growth nonlinear terms	6
Special solutions to the space fractional diffusion problem	6
On approximate controllability of semi-linear neutral integro-differential evolution systems with state-dependent nonlocal conditions	6
Reachability of time-varying fractional dynamical systems with Riemann-Liouville fractional derivative	6
Appell system associated with the infinite dimensional Fractional Pascal measure	6
Pullback dynamics of 2D non-autonomous Reissner-Mindlin-Timoshenko plate systems	6
An inverse problem of determining the fractional order in the TFDE using the measurement at one space-time point	6
Existence, nonexistence and multiplicity of bounded solutions to a nonlinear BVP associated to the fractional Laplacian	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
Unification of popular artificial neural network activation functions	6
Non-stationary zipper $$\alpha $$-fractal functions and associated fractal operator	6
Hopf’s lemma and radial symmetry for the Logarithmic Laplacian problem	6
Hölder regularity for the nonlinear stochastic time-fractional slow & fast diffusion equations on $${\mathbb {R}}^d$$	6
Halanay inequality involving $$\psi -$$Caputo derivative and application to a neural network system	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
A simple series representation for a class of fractal interpolation functions	6
Finding extrema using the unified fractional derivative: a conjecture	6
Identifying source term and initial value simultaneously for the time-fractional diffusion equation with Caputo-like hyper-Bessel operator	5
A time-space fractional parabolic type problem: weak, strong and classical solutions	5
Sticky Brownian motions on star graphs	5
Existence, multiplicity and asymptotic behaviour of normalized solutions to non-autonomous fractional HLS lower critical Choquard equation	5
Generalized fractional operators do not preserve periodicity	5
Fractional Derivatives: the ultimate operator for modelling complex viscoelastic materials?	5
A mutually exciting rough jump-diffusion for financial modelling	5
The Cauchy problem and distribution of local fluctuations of one Riesz gravitational field	5
The existence and averaging principle for Caputo fractional stochastic delay differential systems	5
Collage theorems, invertibility and fractal functions	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
Attractors of Caputo fractional differential equations with triangular vector fields	5
The fractional variation and the precise representative of $$BV^{\alpha ,p}$$ functions	5
Cauchy problem for non-autonomous fractional evolution equations	5
Dependence of solutions on the order of the Caputo-Hadamard derivative and illustrative examples	5
Multiplicity of couple solution for a fractional $$(\varphi , \psi )$$-like system	5
Adaptive finite-time fuzzy composite control for nonlinear fractional-order systems based on complexity avoidance	5
Discrete-time general fractional calculus	5
Strong stationarity for non-smooth control problems with fractional semi-linear elliptic equations in dimension $$N\le 3$$	5
Invariant tori for the fractional nonlinear Schrödinger equation with nonlinearity periodically depending on spatial variable	5
On the existence of solutions for a class of nonlinear fractional Schrödinger-Poisson system: Subcritical and critical cases	5
Mixed fractional stochastic heat equation with additive fractional-colored noise	5
On the computation of the Mittag-Leffler function of fractional powers of accretive operators	4
Asymptotics of the s-fractional Gaussian perimeter as $$s\rightarrow 0^+$$	4
A class of Hilfer fractional differential evolution hemivariational inequalities with history-dependent operators	4
Representations of abstract resolvent families on time scales via Laplace Transform	4
Solvability for a class of two-term nonlinear functional boundary value problems and its applications	4
Comparison principles for the time-fractional diffusion equations with the Robin boundary conditions. Part I: Linear equations	4
Fractional differential equation on the whole axis involving Liouville derivative	4

Fractional Euler numbers and generalized proportional fractional logistic differential equation	4
On the fractional Laplacian of variable order	4
Principal curves to fractional m-Laplacian systems and related maximum and comparison principles	4
Queuing models with Mittag-Leffler inter-event times	4
A bifurcation result for a Keller-Segel-type problem	4
Space-time fractional parabolic equations on a metric star graph with spatial fractional derivative of Sturm-Liouville type: analysis and discretization	4
Existence and multiplicity of positive solutions for a critical fractional Laplacian equation with singular nonlinearity	4
Global solutions of nonlinear fractional diffusion equations with time-singular sources and perturbed orders	4
Localized special John–Nirenberg–Campanato spaces via congruent cubes with applications to boundedness of local Calderón–Zygmund singular integrals and fractional integrals	4
On some even-sequential fractional boundary-value problems	4
Difference Between Riesz Derivative and Fractional Laplacian on the Proper Subset of ℝ	4
Energy stability and convergence of variable-step L1 scheme for the time fractional Swift-Hohenberg model	4
Rich phenomenology of the solutions in a fractional Duffing equation	4
Variable-order fractional 1-Laplacian diffusion equations for multiplicative noise removal	4
Correction: Comparison principles for the time-fractional diffusion equations with the Robin boundary conditions. Part I: Linear equations	4
Sum of series and new relations for Mittag-Leffler functions	4
Abstract fractional inverse source problem of order $$0<\alpha <1$$ in a Banach space	4
Spectral analysis of a family of nonsymmetric fractional elliptic operators	4
Pointwise characterizations of variable Besov and Triebel-Lizorkin spaces via Hajłasz gradients	4
Mixed order elliptic problems driven by a singularity, a Choquard type term and a discontinuous power nonlinearity with critical variable exponents	4
Global solvability of inverse coefficient problem for one fractional diffusion equation with initial non-local and integral overdetermination conditions	4
Skellam and time-changed variants of the generalized fractional counting process	4
Analytical solutions for fractional partial delay differential-algebraic equations with Dirichlet boundary conditions defined on a finite domain	4
Homogenization and inverse problems for fractional diffusion equations	4
Fractional Fokker-Planck-Kolmogorov equations with Hölder continuous drift	4
Asymptotic cycles in fractional maps of arbitrary positive orders	4
A new approach to multi-delay matrix valued fractional linear differential equations with constant coefficients	4
A variational theory for integral functionals involving finite-horizon fractional gradients	4
Topological properties of solution sets for control problems driven by fractional delay differential quasi-hemivariational inequalities and applications	3
On discrete tempered fractional calculus and its application	3
Simulating neuronal dynamics in fractional adaptive exponential integrate-and-fire models	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
Analysis of a class of completely non-local elliptic diffusion operators	3
Nonlinear iterated function systems and fractal interpolation functions with Pata-type contractions	3
Optimized fractional-order Butterworth filter design in complex F-plane	3
A higher order resolvent-positive finite difference approximation for fractional derivatives on bounded domains	3
Computation of the inverse Mittag–Leffler function and its application to modeling ultraslow dynamics	3
An elementary inequality for dissipative Caputo fractional differential equations	3
Impulse response of commensurate fractional-order systems: multiple complex poles	3
Non-homogeneous generalized fractional skellam process	3
Existence and multiplicity of solutions to magnetic Kirchhoff equations in Orlicz-Sobolev spaces	3
Variational methods for nonpositive mixed local–nonlocal operators	3
Analysis and computation for quenching solution to the time-space fractional Kawarada problem	3
No-regret and low-regret controls of space-time fractional parabolic Sturm-Liouville equations in a star graph	3
Generalized fractional Dirac type operators	3
Subordination principle and Feynman-Kac formulae for generalized time-fractional evolution equations	3
Multi-parametric Le Roy function	3
Fractional vector-valued nonuniform MRA and associated wavelet packets on $$L^2\big ({\mathbb {R}},{\mathbb {C}}^M\big )$$	3
Attractors of Caputo semi-dynamical systems	3
Fractional order control for unstable first order processes with time delays	3
An anomalous fractional diffusion operator	3
Applications of Babenko’s method to a class of integral equations	3
Existence and Controllability Results for Hilfer Fractional Evolution Equations via Integral Contractors	3
An inverse problem of determining orders of systems of fractional pseudo-differential equations	3
$$\psi $$-Hilfer type linear fractional differential equations with variable coefficients	3
Topological properties of the solution set for Caputo fractional evolution inclusions involving delay	3
On the Filippov-Ważewski relaxation theorem for a certain class of fractional differential inclusions	3
Existence and uniqueness of discrete weighted pseudo S-asymptotically $$\omega $$-periodic solution to abstract semilinear superdiffusive difference equation	3
The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces II	3
Reconstruction of a fractional evolution equation with a source	3
Fractional integral operators on Orlicz slice Hardy spaces	3
On the kinetics of $$\psi $$-fractional differential equations	3
A spectral approach to non-linear weakly singular fractional integro-differential equations	3
Asymptotical stabilization of fuzzy semilinear dynamic systems involving the generalized Caputo fractional derivative for $$q \in (1,2)$$	3
Wright functions of the second kind and Whittaker functions	3
Lump solutions of the fractional Kadomtsev–Petviashvili equation	2
On the variable order fractional calculus of fractal interpolation functions	2
Multiple solutions for anisotropic nonlocal problems with variable exponents	2
RETRACTED ARTICLE: Averaging principle for stochastic Caputo fractional differential equations with non-Lipschitz condition	2
On mild solutions of the generalized nonlinear fractional pseudo-parabolic equation with a nonlocal condition	2
Some boundedness results for Riemann-Liouville tempered fractional integrals	2
Some Properties of the Fractal Convolution of Functions	2
Least energy sign-changing solutions for fractional critical Kirchhoff–Schrödinger–Poisson with steep potential well	2
Inverse coefficient problems for the heat equation with fractional Laplacian	2
The overdamped generalized Langevin equation with Hermite noise	2
An improved fractional predictor-corrector method for nonlinear fractional differential equations with initial singularity	2
Remarks on the nonlinear fractional Choquard equation	2
Initial-boundary value problems for multi-term time-fractional wave equations	2
Measure attractors of asymptotic autonomy fractional stochastic reaction-diffusion equations on unbounded domains	2
Ground states for p-fractional Choquard-type equations with doubly or triply critical nonlinearity	2
CTRW modeling of quantum measurement and fractional equations of quantum stochastic filtering and control	2
On variable-order fractional linear viscoelasticity	2
Group classification of time fractional Black-Scholes equation with time-dependent coefficients	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
Existence of positive solutions for fractional delayed evolution equations of order $$\gamma \in (1,2)$$ via measure of non-compactness	2
The similarity method and explicit solutions for the fractional space one-phase Stefan problems	2
Pricing Vulnerable Options in Fractional Brownian Markets: a Partial Differential Equations Approach	2
Dynamical repulsive fractional potential fields in 3D environment	2
Time optimal controls for Hilfer fractional evolution equations	2
Fractional Sobolev type spaces of functions of two variables via Riemann-Liouville derivatives	2
Multiplicity of solutions for fractional Hamiltonian systems with combined nonlinearities and without coercive conditions	2
Ground state solution for a generalized Choquard Schr$$\ddot{\text {o}}$$dinger equation with vanishing potential in homogeneous fractional Musielak Sobolev spaces	2
The oscillatory solutions of multi-order fractional differential equations	2
Two families of second-order fractional numerical formulas and applications to fractional differential equations	2