Fractional Calculus and Applied Analysis

Article	Citations
Sonine-Dimovski transform and spectral synthesis associated with the hyper-Bessel operator on the complex plane	42
Bounds for mixing times for finite semi-Markov processes with heavy-tail jump distribution	39
Blow-up for a non-linear stable non-Gaussian process in fractional time	31
Analysis of BURA and BURA-based approximations of fractional powers of sparse SPD matrices	29
Symmetry of solutions for asymptotically symmetric nonlocal parabolic equations	28
On generalized K-functionals in $$L_p$$ for $$0<p<1$$	28
Differential transforms related to Caputo time-fractional derivatives and semigroups generated by fractional Schrödinger operators	26
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	24
Fractional differential equations of Bagley-Torvik and Langevin type	24
Stochastic heat equation driven by space-only fractional Lévy noise	23
Rigidity of phase transitions for the fractional elliptic Gross-Pitaevskii system	22
A review of constitutive models for non-Newtonian fluids	19
Stability analysis of Hilfer fractional stochastic switched dynamical systems with non-Gaussian process and impulsive effects	19
Considerations regarding the accuracy of fractional numerical computations	19
Asymptotically autonomous dynamics for fractional subcritical nonclassical diffusion equations driven by nonlinear colored noise	19
The Spatially Variant Fractional Laplacian	19
On heat equations associated with fractional harmonic oscillators	19
Multi-parametric Le Roy function revisited	18
Differentiation of integral Mittag-Leffler and integral Wright functions with respect to parameters	16
Dual Spaces of Anisotropic Variable Hardy–Lorentz Spaces and Their Applications	16
Delsarte equation for Caputo operator of fractional calculus	16
Fractional differential operators, fractional Sobolev spaces and fractional variation on homogeneous Carnot groups	16
Multi-term fractional oscillation integro-differential equations	16
Representations of solutions of systems of time-fractional pseudo-differential equations	15

Mixed slow-fast stochastic differential equations: Averaging principle result	14
Abstract multi-term fractional difference equations	14
Asymptotic analysis of three-parameter Mittag-Leffler function with large parameters, and application to sub-diffusion equation involving Bessel operator	14
On approximate controllability of multi-term time fractional measure differential equations with nonlocal conditions	14
Towards a Unified theory of Fractional and Nonlocal Vector Calculus	13
Two disjoint and infinite sets of solutions for a concave-convex critical fractional Laplacian equation	13
A Fractional Order Derivative Newton-Raphson Method for the Computation of the Power Flow Problem Solution in Energy Systems	13
Radial symmetry and Hopf lemma for fully nonlinear parabolic equations involving the fractional Laplacian	13
Concentration phenomenon of solutions for fractional Choquard equations with upper critical growth	12
Decay estimates and extinction properties for some parabolic equations with fractional time derivatives	12
The well-posedness analysis in Besov-type spaces for multi-term time-fractional wave equations	12
Infinitely many sign-changing solutions for a kind of fractional Klein-Gordon-Maxwell system	12
The fractional stochastic heat equation driven by time-space white noise	12
Fractional boundary value problems and elastic sticky brownian motions	11
Fractional Wiener chaos: Part 1	11
Radial symmetry and Liouville theorem for master equations	11
A high order predictor-corrector method with non-uniform meshes for fractional differential equations	11
Initial-boundary value problems for coupled systems of time-fractional diffusion equations	10
Generalized fractional derivatives generated by Dickman subordinator and related stochastic processes	10
A unified analysis framework for generalized fractional Moore–Gibson–Thompson equations: Well-posedness and singular limits	10
Limitations and applications in a fractional Barbalat’s Lemma	10
Controllability of Hilfer fractional backward evolution systems	10
Fractional models for analysis of economic risks	10
On the convergence of the Galerkin method for random fractional differential equations	9
A critical elliptic problem involving exponential and singular nonlinearities	9
Riemann-Liouville derivatives of abstract functions and Sobolev spaces	9
Analysis of a fractional viscoelastic Euler-Bernoulli beam and identification of its piecewise continuous polynomial order	9
On the Decomposition of Solutions: From Fractional Diffusion to Fractional Laplacian	9
On the multivariate generalized counting process and its time-changed variants	9
Weighted estimates for operators of fractional integration of variable order in generalized variable Hölder spaces	9
Integral operators defined “up to a polynomial”	9
A unified way to solve IVPs and IBVPs for the time-fractional diffusion-wave equation	9
Superlinear solutions of sublinear fractional differential equations and regular variation	9
Boundedness of fractional integrals on special John–Nirenberg–Campanato and Hardy-type spaces via congruent cubes	9
Controllability and observability of linear time-varying fractional systems	9
On the existence and uniqueness of the solution to multifractional stochastic delay differential equation	8
Log-concavity and log-convexity of series containing multiple Pochhammer symbols	8
Concave-convex critical problems for the spectral fractional laplacian with mixed boundary conditions	8
Fractional-order problem coupled with a second-order Moreau’s sweeping process	8
A Strong Maximum Principle for the Fractional Laplace Equation with Mixed Boundary Condition	8
Explicit Representation of Discrete Fractional Resolvent Families in Banach Spaces	8
Correction: Existence, uniqueness and regularity for a semilinear stochastic subdiffusion with integrated multiplicative noise	8
Fractional Musielak-Sobolev spaces: study of generalized double phase problem with Choquard-logarithmic nonlinearity	8
Convergence to logarithmic-type functions of solutions of fractional systems with Caputo-Hadamard and Hadamard fractional derivatives	8
Vallée-Poussin theorem for fractional functional differential equations	8
Analysis and Fast Approximation of a Steady-State Spatially-Dependent Distributed-order Space-Fractional Diffusion Equation	8
Summability of Formal Solutions for a Family of Generalized Moment Integro-Differential Equations	8
From time to times	8
Abstract fractional linear pseudo-parabolic equations in Banach spaces: well-posedness, regularity, and asymptotic behavior	8
Approximate solutions for fractional stochastic integro-differential equation with short memory driven by non-instantaneous impulses	8

Convergence Rate Estimates for the Kernelized Predictor Corrector Method for Fractional Order Initial Value Problems	7
A semilinear diffusion PDE with variable order time-fractional Caputo derivative subject to homogeneous Dirichlet boundary conditions	7
The sliding method for fractional Laplacian systems	7
B-Spline Collocation Discretizations of Caputo and Riemann-Liouville Derivatives: A Matrix Comparison	7
Continuous-time MISO fractional system identification using higher-order-statistics	7
Study on the diffusion fractional m-Laplacian with singular potential term	7
Some nonexistence results for space–time fractional Schrödinger equations without gauge invariance	7
Convolution series and the generalized convolution Taylor formula	7
Nonlocal Kirchhoff-type problems with singular nonlinearity: existence, uniqueness and bifurcation	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
Stability and stabilization of short memory fractional differential equations with delayed impulses	7
Sequential generalized Riemann–Liouville derivatives based on distributional convolution	7
Multiplicity of solutions for a fractional Kirchhoff type equation with a critical nonlocal term	7
Numerical scheme for Erdélyi–Kober fractional diffusion equation using Galerkin–Hermite method	7
Anisotropic variable Campanato-type spaces and their Carleson measure characterizations	7
Special solutions to the space fractional diffusion problem	6
An efficient numerical method to the stochastic fractional heat equation with random coefficients and fractionally integrated multiplicative noise	6
A tempered subdiffusive Black–Scholes model	6
Monotonicity and uniqueness of positive solutions to elliptic fractional p-equations	6
A fractional version of the recursive Tau method for solving a general class of Abel-Volterra integral equations systems	6
Hölder regularity for the nonlinear stochastic time-fractional slow & fast diffusion equations on $${\mathbb {R}}^d$$	6
Appell system associated with the infinite dimensional Fractional Pascal measure	6
Existence, nonexistence and multiplicity of bounded solutions to a nonlinear BVP associated to the fractional Laplacian	6
Operational matrix based numerical scheme for the solution of time fractional diffusion equations	6
A fast fractional block-centered finite difference method for two-sided space-fractional diffusion equations on general nonuniform grids	6
The nonlinear fractional Rayleigh-Stokes problem on an infinite interval	6
Existence and uniqueness of a weak solution to fractional single-phase-lag heat equation	6
A second-order fitted scheme for time fractional telegraph equations involving weak singularity	6
Non-stationary zipper $$\alpha $$-fractal functions and associated fractal operator	6
Existence and asymptotic behavior of square-mean S-asymptotically periodic solutions for fractional stochastic evolution equation with delay	6
On the three dimensional generalized Navier-Stokes equations with damping	6
Monte Carlo method for fractional-order differentiation	6
S-asymptotically $$\omega $$-periodic solutions for time-space fractional nonlocal reaction-diffusion equation with superlinear growth nonlinear terms	6
Fractional boundary value problems	6
An inverse problem of determining the fractional order in the TFDE using the measurement at one space-time point	6
Schrödinger-Maxwell equations driven by mixed local-nonlocal operators	6
On approximate controllability of semi-linear neutral integro-differential evolution systems with state-dependent nonlocal conditions	6
Unification of popular artificial neural network activation functions	6
Game-theoretical problems for fractional-order nonstationary systems	6
Infinitely many large solutions to a variable order nonlocal singular equation	6
Pricing European option under the generalized fractional jump-diffusion model	5
Attractors of Caputo fractional differential equations with triangular vector fields	5
Sticky Brownian motions on star graphs	5
Pullback dynamics of 2D non-autonomous Reissner-Mindlin-Timoshenko plate systems	5
Subordination and memory dependent kinetics in diffusion and relaxation phenomena	5
A mutually exciting rough jump-diffusion for financial modelling	5
On the existence of solutions for a class of nonlinear fractional Schrödinger-Poisson system: Subcritical and critical cases	5
On the Green Function of the Killed Fractional Laplacian on the Periodic Domain	5
Existence, multiplicity and asymptotic behaviour of normalized solutions to non-autonomous fractional HLS lower critical Choquard equation	5
Collage theorems, invertibility and fractal functions	5
Mixed fractional stochastic heat equation with additive fractional-colored noise	5
The Cauchy problem and distribution of local fluctuations of one Riesz gravitational field	5
Reachability of time-varying fractional dynamical systems with Riemann-Liouville fractional derivative	5
A time-space fractional parabolic type problem: weak, strong and classical solutions	5
Identifying source term and initial value simultaneously for the time-fractional diffusion equation with Caputo-like hyper-Bessel operator	5
The fractional variation and the precise representative of $$BV^{\alpha ,p}$$ functions	5
Strong stationarity for non-smooth control problems with fractional semi-linear elliptic equations in dimension $$N\le 3$$	5
Discrete-time general fractional calculus	5
Cauchy problem for non-autonomous fractional evolution equations	5
The existence and averaging principle for Caputo fractional stochastic delay differential systems	5
Hopf’s lemma and radial symmetry for the Logarithmic Laplacian problem	5
Finding extrema using the unified fractional derivative: a conjecture	5
Multiplicity of couple solution for a fractional $$(\varphi , \psi )$$-like system	5
Global optimization of a nonlinear system of differential equations involving $$\psi $$-Hilfer fractional derivatives of complex order	5
Fractional Fokker-Planck-Kolmogorov equations with Hölder continuous drift	4
Representations of abstract resolvent families on time scales via Laplace Transform	4
Comparison principles for the time-fractional diffusion equations with the Robin boundary conditions. Part I: Linear equations	4
Queuing models with Mittag-Leffler inter-event times	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
Existence and multiplicity of positive solutions for a critical fractional Laplacian equation with singular nonlinearity	4
Invariant tori for the fractional nonlinear Schrödinger equation with nonlinearity periodically depending on spatial variable	4
Generalized fractional operators do not preserve periodicity	4
Global solutions of nonlinear fractional diffusion equations with time-singular sources and perturbed orders	4
On some even-sequential fractional boundary-value problems	4
Energy stability and convergence of variable-step L1 scheme for the time fractional Swift-Hohenberg model	4
A new approach to multi-delay matrix valued fractional linear differential equations with constant coefficients	4
Analytical solutions for fractional partial delay differential-algebraic equations with Dirichlet boundary conditions defined on a finite domain	4

Spectral analysis of a family of nonsymmetric fractional elliptic operators	4
A class of Hilfer fractional differential evolution hemivariational inequalities with history-dependent operators	4
Difference Between Riesz Derivative and Fractional Laplacian on the Proper Subset of ℝ	4
Adaptive finite-time fuzzy composite control for nonlinear fractional-order systems based on complexity avoidance	4
Asymptotics of the s-fractional Gaussian perimeter as $$s\rightarrow 0^+$$	4
Fractional differential equation on the whole axis involving Liouville derivative	4
On the fractional Laplacian of variable order	4
Skellam and time-changed variants of the generalized fractional counting process	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
A variational theory for integral functionals involving finite-horizon fractional gradients	4
Space-time fractional parabolic equations on a metric star graph with spatial fractional derivative of Sturm-Liouville type: analysis and discretization	4
A bifurcation result for a Keller-Segel-type problem	4
On the computation of the Mittag-Leffler function of fractional powers of accretive operators	4
Principal curves to fractional m-Laplacian systems and related maximum and comparison principles	4
Global solvability of inverse coefficient problem for one fractional diffusion equation with initial non-local and integral overdetermination conditions	3
Localized special John–Nirenberg–Campanato spaces via congruent cubes with applications to boundedness of local Calderón–Zygmund singular integrals and fractional integrals	3
A higher order resolvent-positive finite difference approximation for fractional derivatives on bounded domains	3
Attractors of Caputo semi-dynamical systems	3
Applications of a new measure of noncompactness to the solvability of systems of nonlinear and fractional integral equations in the generalized Morrey spaces	3
Topological properties of the solution set for Caputo fractional evolution inclusions involving delay	3
Wright functions of the second kind and Whittaker functions	3
Optimized fractional-order Butterworth filter design in complex F-plane	3
Generalized fractional Dirac type operators	3
Existence and multiplicity of solutions to magnetic Kirchhoff equations in Orlicz-Sobolev spaces	3
Fractional integral operators on Orlicz slice Hardy spaces	3
Impulse response of commensurate fractional-order systems: multiple complex poles	3
On the kinetics of $$\psi $$-fractional differential equations	3
Asymptotic cycles in fractional maps of arbitrary positive orders	3
Homogenization and inverse problems for fractional diffusion equations	3
Variable-order fractional 1-Laplacian diffusion equations for multiplicative noise removal	3
Asymptotical stabilization of fuzzy semilinear dynamic systems involving the generalized Caputo fractional derivative for $$q \in (1,2)$$	3
Multi-parametric Le Roy function	3
FCAA Related News, Events and Books (FCAA-Volume 24-5-2021)	3
$$\psi $$-Hilfer type linear fractional differential equations with variable coefficients	3
Computation of the inverse Mittag–Leffler function and its application to modeling ultraslow dynamics	3
Simulating neuronal dynamics in fractional adaptive exponential integrate-and-fire models	3
On the Filippov-Ważewski relaxation theorem for a certain class of fractional differential inclusions	3
An inverse problem of determining orders of systems of fractional pseudo-differential equations	3
A spectral approach to non-linear weakly singular fractional integro-differential equations	3
An elementary inequality for dissipative Caputo fractional differential equations	3
An anomalous fractional diffusion operator	3
Mixed order elliptic problems driven by a singularity, a Choquard type term and a discontinuous power nonlinearity with critical variable exponents	3
Fractional order control for unstable first order processes with time delays	3
Fractional Euler numbers and generalized proportional fractional logistic differential equation	3
Fractional vector-valued nonuniform MRA and associated wavelet packets on $$L^2\big ({\mathbb {R}},{\mathbb {C}}^M\big )$$	3
Topological properties of solution sets for control problems driven by fractional delay differential quasi-hemivariational inequalities and applications	3
Existence and uniqueness of discrete weighted pseudo S-asymptotically $$\omega $$-periodic solution to abstract semilinear superdiffusive difference equation	3
No-regret and low-regret controls of space-time fractional parabolic Sturm-Liouville equations in a star graph	3
Analysis of a class of completely non-local elliptic diffusion operators	3
The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces II	3
On discrete tempered fractional calculus and its application	3
Reconstruction of a fractional evolution equation with a source	3
Solvability for a class of two-term nonlinear functional boundary value problems and its applications	3
Nonlinear iterated function systems and fractal interpolation functions with Pata-type contractions	3
The oscillatory solutions of multi-order fractional differential equations	2
Multiplicity of solutions for fractional Hamiltonian systems with combined nonlinearities and without coercive conditions	2
The overdamped generalized Langevin equation with Hermite noise	2
Fractional Sobolev type spaces of functions of two variables via Riemann-Liouville derivatives	2
On the variable order fractional calculus of fractal interpolation functions	2
A Meyer-Itô formula for stable processes via fractional calculus	2
An improved fractional predictor-corrector method for nonlinear fractional differential equations with initial singularity	2
Variational methods for nonpositive mixed local–nonlocal operators	2
Dynamical repulsive fractional potential fields in 3D environment	2
Hölder regularity for non-autonomous fractional evolution equations	2
Convergence analysis of the time-stepping numerical methods for time-fractional nonlinear subdiffusion equations	2
Solvability of infinite systems of fractional differential equations in the double sequence space $$ 2^c(\triangle )$$	2
Approximation with continuous functions preserving fractal dimensions of the Riemann-Liouville operators of fractional calculus	2
Inverse coefficient problems for the heat equation with fractional Laplacian	2
Some Properties of the Fractal Convolution of Functions	2
Prabhakar function of Le Roy type: a set of results in the complex plane	2
On mild solutions of the generalized nonlinear fractional pseudo-parabolic equation with a nonlocal condition	2
Relative controllability of linear state-delay fractional systems	2
Lump solutions of the fractional Kadomtsev–Petviashvili equation	2
Existence and Controllability Results for Hilfer Fractional Evolution Equations via Integral Contractors	2
Orlicz-Lorentz-Karamata Hardy martingale spaces: inequalities and fractional integral operators	2
Subordination principle and Feynman-Kac formulae for generalized time-fractional evolution equations	2
Pricing Vulnerable Options in Fractional Brownian Markets: a Partial Differential Equations Approach	2
Inverse problem to determine simultaneously several scalar parameters and a time-dependent source term in a superdiffusion equation involving a multiterm fractional Laplacian	2
Two families of second-order fractional numerical formulas and applications to fractional differential equations	2
CTRW modeling of quantum measurement and fractional equations of quantum stochastic filtering and control	2
Final value problem for Rayleigh-Stokes type equations involving weak-valued nonlinearities	2
Ground state solution for a generalized Choquard Schr$$\ddot{\text {o}}$$dinger equation with vanishing potential in homogeneous fractional Musielak Sobolev spaces	2
Weighted boundedness of fractional integrals associated with admissible functions on spaces of homogeneous type	2
RETRACTED ARTICLE: Averaging principle for stochastic Caputo fractional differential equations with non-Lipschitz condition	2
Initial-boundary value problems for multi-term time-fractional wave equations	2
Properties of the multi-index special function $${\mathcal {W}}^{\left( \bar{\alpha },\bar{\nu }\right) }(z)$$	2
Ground states for p-fractional Choquard-type equations with doubly or triply critical nonlinearity	2
Analysis and computation for quenching solution to the time-space fractional Kawarada problem	2
Existence of positive solutions for fractional delayed evolution equations of order $$\gamma \in (1,2)$$ via measure of non-compactness	2
System of fractional boundary value problems at resonance	2
The similarity method and explicit solutions for the fractional space one-phase Stefan problems	2
Nehari manifold approach for fractional Kirchhoff problems with extremal value of the parameter	2
Some boundedness results for Riemann-Liouville tempered fractional integrals	2
Least energy sign-changing solutions for fractional critical Kirchhoff–Schrödinger–Poisson with steep potential well	2