Fractional Calculus and Applied Analysis

Article	Citations
Why Fractional Derivatives with Nonsingular Kernels Should Not Be Used	86
Operational Calculus for the General Fractional Derivative and Its Applications	67
Fractional Derivatives and the Fundamental Theorem of Fractional Calculus	40
Completely Monotone Multinomial Mittag-Leffler Type Functions and Diffusion Equations with Multiple Time-Derivatives	29
An efficient localized collocation solver for anomalous diffusion on surfaces	29
ContribUtions on Artificial Potential Field Method for Effective Obstacle Avoidance	26
Degenerate Kirchhoff (p, q)–Fractional Systems with Critical Nonlinearities	25
A Class of Linear Non-Homogenous Higher Order Matrix Fractional Differential Equations: Analytical Solutions and New Technique	25
Determination of the Order of Fractional Derivative for Subdiffusion Equations	23
On the kinetics of Hadamard-type fractional differential systems	23
A Cauchy problem for fractional evolution equations with Hilfer’s fractional derivative on semi-infinite interval	22
On a Non–Local Problem for a Multi–Term Fractional Diffusion-Wave Equation	21
Towards a Unified theory of Fractional and Nonlocal Vector Calculus	21
Convolution series and the generalized convolution Taylor formula	21
On Representation Formulas for Solutions of Linear Differential Equations with Caputo Fractional Derivatives	20
A Survey on Numerical Methods for Spectral Space-Fractional Diffusion Problems	20
An Inverse Problem Approach to Determine Possible Memory Length of Fractional Differential Equations	19
Operational Calculus for the Riemann–Liouville Fractional Derivative with Respect to a Function and its Applications	18
Unified predictor–corrector method for fractional differential equations with general kernel functions	18
Fractional Derivatives and Cauchy Problem for Differential Equations of Fractional Order	16
Well-Posedness for Weak and Strong Solutions of Non-Homogeneous Initial Boundary Value Problems for Fractional Diffusion Equations	16
New finite-time stability analysis of singular fractional differential equations with time-varying delay	16
Attractivity for Differential Equations of Fractional order and ψ-Hilfer Type	16
Asymptotic stability of fractional difference equations with bounded time delays	15
Hölder regularity for non-autonomous fractional evolution equations	15

Fractional Euler numbers and generalized proportional fractional logistic differential equation	15
Box dimension of mixed Katugampola fractional integral of two-dimensional continuous functions	15
Non-stationary zipper $$\alpha $$-fractal functions and associated fractal operator	13
Fractional-Order Susceptible-Infected Model: Definition and Applications to the Study of COVID-19 Main Protease	13
An Averaging Principle For Stochastic Differential Equations Of Fractional Order 0 < α < 1	13
Generalized Fractional Poisson Process and Related Stochastic Dynamics	13
The continuation of solutions to systems of Caputo fractional order differential equations	13
Convergence analysis of the time-stepping numerical methods for time-fractional nonlinear subdiffusion equations	12
The Bouncing Ball and the Grünwald-Letnikov Definition of Fractional Derivative	12
Inverse Problem for a Multi-Term Fractional Differential Equation	12
Inverse Problems for Diffusion Equation with Fractional Dzherbashian-Nersesian Operator	12
SHould I Stay Or Should I Go? Zero-Size Jumps in Random Walks for Lévy Flights	12
Optimal feedback control for a class of fractional evolution equations with history-dependent operators	12
Fractional integral operators on Orlicz slice Hardy spaces	11
Characterizations of Variable Martingale Hardy Spaces Via Maximal Functions	11
Exact Stability and Instability Regions for Two-Dimensional Linear Autonomous Multi-Order Systems of Fractional-Order Differential Equations	11
The Crank-Nicolson Type Compact Difference Schemes for a Loaded Time-Fractional Hallaire Equation	11
Three Representations of the Fractional p-Laplacian: Semigroup, Extension and Balakrishnan Formulas	11
Error Analysis of Nonlinear Time Fractional Mobile/Immobile Advection-Diffusion Equation with Weakly Singular Solutions	11
Uniqueness for an Inverse Source Problem of Determining a Space-Dependent Source in a Non-Autonomous Time-Fractional Diffusion Equation	11
Analysis of Fractional Integro-Differential Equations with Nonlocal Erdélyi-Kober Type Integral Boundary Conditions	11
Variational Methods to the p-Laplacian type Nonlinear Fractional Order Impulsive Differential Equations with Sturm-Liouville Boundary-Value Problem	10
Applications of Hilfer-Prabhakar Operator to Option Pricing Financial Model	9
Analytical and dimensional properties of fractal interpolation functions on the Sierpiński gasket	9
The Green Function for a Class of Caputo Fractional Differential Equations with a Convection Term	9
Cauchy Problem for General Time Fractional Diffusion Equation	9
The fractional-order Lorenz-type systems: A review	9
Recent Developments on the Realization of Fractance Device	9
Output Error MISO System Identification Using Fractional Models	9
Analysis of Solutions of Some Multi-Term Fractional Bessel Equations	8
Stability analysis of Hadamard and Caputo-Hadamard fractional nonlinear systems without and with delay	8
Two High-Order Time Discretization Schemes for Subdiffusion Problems with Nonsmooth Data	8
Determination of the Fractional Order in Semilinear Subdiffusion Equations	8
Approximate inversion for Abel integral operators of variable exponent and applications to fractional Cauchy problems	8
Time-changed fractional Ornstein-Uhlenbeck process	8
The fractional variation and the precise representative of $$BV^{\alpha ,p}$$ functions	8
Nontrivial Solutions of Non-Autonomous Dirichlet Fractional Discrete Problems	7
Multiple Positive Solutions for a Nonlocal Pde with Critical Sobolev-Hardy and Singular Nonlinearities Via Perturbation Method.	7
Upper and lower estimates for the separation of solutions to fractional differential equations	7
Exact solutions of fractional oscillation systems with pure delay	7
Multivariate Fractional Phase—Type Distributions	7
On a Method of Solution of Systems of Fractional Pseudo-Differential Equations	6
Fractional vector-valued nonuniform MRA and associated wavelet packets on $$L^2\big ({\mathbb {R}},{\mathbb {C}}^M\big )$$	6
Fractional Integro-Differential Equations in Wiener Spaces	6
On the fractional Laplacian of variable order	6
Wave Propagation Dynamics in a Fractional Zener Model with Stochastic Excitation	6
Stability Analysis for Discrete Time Abstract Fractional Differential Equations	6
Boundedness of fractional integrals on special John–Nirenberg–Campanato and Hardy-type spaces via congruent cubes	6
Asymptotic cycles in fractional maps of arbitrary positive orders	6
Approximate controllability results for the Sobolev type fractional delay impulsive integrodifferential inclusions of order $${r} \in (1,2)$$ via sectorial operator	6

Monte Carlo method for fractional-order differentiation extended to higher orders	6
Existence and Controllability Results for Hilfer Fractional Evolution Equations via Integral Contractors	6
RenoRmalization Group and Fractional Calculus Methods in a Complex World: A Review	6
Green’s Function for the Fractional KDV Equation on the Periodic Domain via Mittag-Leffler Function	6
Variational Approximation for Fractional Sturm–Liouville Problem	6
Caputo delta weakly fractional difference equations	5
An inverse problem of determining orders of systems of fractional pseudo-differential equations	5
Short time coupled fractional fourier transform and the uncertainty principle	5
Tempered Relaxation Equation and Related Generalized Stable Processes	5
(N + α)-Order low-pass and high-pass filter transfer functions for non-cascade implementations approximating butterworth response	5
AsymptotIc Behavior of Solutions of Fractional Differential Equations with Hadamard Fractional Derivatives	5
Solution of Linear Fractional Order Systems with Variable Coefficients	5
Optimized fractional-order Butterworth filter design in complex F-plane	5
Multi-parametric Le Roy function	5
Some Properties of the Fractal Convolution of Functions	5
Regularity Results for Nonlocal Evolution Venttsel’ Problems	5
Finite-approximate controllability of impulsive $$\psi -$$Caputo fractional evolution equations with nonlocal conditions	5
Subordination principle for fractional diffusion-wave equations of Sobolev type	5
Duality Theory of Fractional Resolvents and Applications to Backward Fractional Control Systems	5
Exact solutions and Hyers-Ulam stability of fractional equations with double delays	5
Implementation of Fractional Optimal Control Problems in Real-World Applications	5
Subordination and memory dependent kinetics in diffusion and relaxation phenomena	5
Two disjoint and infinite sets of solutions for a concave-convex critical fractional Laplacian equation	5
Global solutions of nonlinear fractional diffusion equations with time-singular sources and perturbed orders	4
Fractional boundary value problems	4
Semilinear Fractional Elliptic Problems with Mixed Dirichlet-Neumann Boundary Conditions	4
Spectral analysis of multifractional LRD functional time series	4
Numerical scheme for Erdélyi–Kober fractional diffusion equation using Galerkin–Hermite method	4
Monte Carlo Estimation of the Solution of Fractional Partial Differential Equations	4
Connections between nonlocal operators: from vector calculus identities to a fractional Helmholtz decomposition	4
Wright functions of the second kind and Whittaker functions	4
Impulse response of commensurate fractional-order systems: multiple complex poles	4
Two families of second-order fractional numerical formulas and applications to fractional differential equations	4
Initial-boundary value problems for coupled systems of time-fractional diffusion equations	4
Anisotropic variable Campanato-type spaces and their Carleson measure characterizations	4
Stochastic solutions of generalized time-fractional evolution equations	4
Sequential generalized Riemann–Liouville derivatives based on distributional convolution	4
Simultaneous inversion for the fractional exponents in the space-time fractional diffusion equation $$\partial _t^\beta u = - {\left( { - \Delta } \right)^{\alpha /2}}u - {\left( { - \Delta } \right)^	4
Optimal F-domain stabilization technique for reduction of commensurate fractional-order SISO systems	4
Subordination principle and Feynman-Kac formulae for generalized time-fractional evolution equations	4
Fractional problems with critical nonlinearities by a sublinear perturbation	4
Properties of the Set of Admissible “State Control” Pair for a Class of Fractional Semilinear Evolution Control Systems	4
Multiple positive solutions for higher-order fractional integral boundary value problems with singularity on space variable	4
On mild solutions of the generalized nonlinear fractional pseudo-parabolic equation with a nonlocal condition	4
Determination of Time-Dependent Sources and Parameters of Nonlocal Diffusion and Wave Equations from Final Data	4
Discrete Fractional Boundary Value Problems and Inequalities	4
Sensitivity analysis for a fractional stochastic differential equation with $$S^{p}$$-weighted pseudo almost periodic coefficients and infinite delay	4
Sliding methods for the higher order fractional laplacians	4
Computation of the inverse Mittag–Leffler function and its application to modeling ultraslow dynamics	4
Summability of Formal Solutions for a Family of Generalized Moment Integro-Differential Equations	4
Maximum Principles and Applications for Fractional Differential Equations with Operators Involving Mittag-Leffler Function	4
Fractional characteristic functions, and a fractional calculus approach for moments of random variables	3
On the Harmonic Extension Approach to Fractional Powers in Banach Spaces	3
Bounded Solutions of Second Order of Accuracy Difference Schemes for Semilinear Fractional Schrödinger Equations	3
Solvability of an infinite system of Langevin fractional differential equations in a new tempered sequence space	3
Monte Carlo method for fractional-order differentiation	3
Analytical solutions for fractional partial delay differential-algebraic equations with Dirichlet boundary conditions defined on a finite domain	3
Differentiation of integral Mittag-Leffler and integral Wright functions with respect to parameters	3
Variational methods for nonpositive mixed local–nonlocal operators	3
A Fractional Analysis in Higher Dimensions for the Sturm-Liouville Problem	3
Existence of Solutions for the Semilinear Abstract Cauchy Problem of Fractional Order	3
Mixed order elliptic problems driven by a singularity, a Choquard type term and a discontinuous power nonlinearity with critical variable exponents	3
Hölder regularity for the nonlinear stochastic time-fractional slow & fast diffusion equations on $${\mathbb {R}}^d$$	3
Initial-value / Nonlocal Cauchy Problems for Fractional Differential Equations Involving ψ-Hilfer Multivariable Operators	3
A fractional version of the recursive Tau method for solving a general class of Abel-Volterra integral equations systems	3
Self-Similar Cauchy Problems and Generalized Mittag-Leffler Functions	3
Maximum Principles for a Class of Generalized Time-Fractional Diffusion Equations	3
A Strong Maximum Principle for the Fractional Laplace Equation with Mixed Boundary Condition	3
Global existence and large time behavior of solutions of a time fractional reaction diffusion system	3
Cauchy problem for non-autonomous fractional evolution equations	3
Mkhitar Djrbashian and His Contribution to Fractional Calculus	3
Prabhakar function of Le Roy type: a set of results in the complex plane	3
On the Decomposition of Solutions: From Fractional Diffusion to Fractional Laplacian	3
Initial-boundary value problems for multi-term time-fractional wave equations	3
System of fractional boundary value problems at resonance	3
A Boundary Value Problem for a Partial Differential Equation with Fractional Derivative	3
Applications of Erdélyi-Kober Fractional Integral for Solving Time-Fractional Tricomi-Keldysh Type Equation	3
A novel approach to stability analysis of a wide class of irrational linear systems	2
An eigenvalue problem in fractional h-discrete calculus	2
Multi-term fractional integro-differential equations in power growth function spaces	2

The Rate of Convergence on Fractional Power Dissipative Operator on Compact Manifolds	2
Mellin definition of the fractional Laplacian	2
Existence for a class of time-fractional evolutionary equations with applications involving weakly continuous operator	2
Approximate Controllability for Stochastic Fractional Hemivariational Inequalities of Degenerate Type	2
Asymptotic behaviour of solutions to non-commensurate fractional-order planar systems	2
The existence and averaging principle for Caputo fractional stochastic delay differential systems	2
Numerical conservation laws of time fractional diffusion PDEs	2
Existence of Local Solutions for Fractional Difference Equations with Left Focal Boundary Conditions	2
Discrete fractional distributed Halanay inequality and applications in discrete fractional order neural network systems	2
Construction of Fixed Point Operators for Nonlinear Difference Equations Of Non Integer Order with Impulses	2
Extremal mild solutions to Hilfer evolution equations with non-instantaneous impulses and nonlocal conditions	2
Robust Fractional-Order Perfect Control for Non-Full Rank Plants Described in the Grünwald-Letnikov IMC Framework	2
On the Green Function of the Killed Fractional Laplacian on the Periodic Domain	2
Bounds for mixing times for finite semi-Markov processes with heavy-tail jump distribution	2
Existence and multiplicity of solutions to magnetic Kirchhoff equations in Orlicz-Sobolev spaces	2
On solvability for a class of nonlinear systems of differential equations with the Caputo fractional derivative	2
Riesz Potentials and Orthogonal Radon Transforms on Affine Grassmannians	2
A new Bihari inequality and initial value problems of first order fractional differential equations	2
Erdélyi–Kober Fractional Integrals and Radon Transforms for Mutually Orthogonal Affine Planes	2
Superlinear solutions of sublinear fractional differential equations and regular variation	2
Nonlinear convolution integro-differential equation with variable coefficient	2
Weak Solvability of the Variable-Order Subdiffusion Equation	2
New fractional maximal operators in the theory of martingale Hardy and Lebesgue spaces with variable exponents	2
Averaging Theory for Fractional Differential Equations	2
Final value problem for Rayleigh-Stokes type equations involving weak-valued nonlinearities	2
On approximate controllability of multi-term time fractional measure differential equations with nonlocal conditions	2
Solvability of infinite systems of fractional differential equations in the double sequence space $$ 2^c(\triangle )$$	2
Construction and analysis of series solutions for fractional quasi-Bessel equations	2
Some estimates for $$p$$-adic fractional integral operator and its commutators on $$p$$-adic Herz spaces with rough kernels	2
“Fuzzy” Calculus: The Link Between Quantum Mechanics and Discrete Fractional Operators	2
Explicit Representation of Discrete Fractional Resolvent Families in Banach Spaces	2
Fractional Diffusion-Wave Equations: Hidden Regularity for Weak Solutions	2
On a Solution of a Fractional Hyper-Bessel Differential Equation by Means of a Multi-Index Special Function	2
Fractional Abstract Cauchy Problem on Complex Interpolation Scales	2
Asymptotic profile for a two-terms time fractional diffusion problem	2
Multidimensional van der Corput-Type Estimates Involving Mittag-Leffler Functions	2
Dynamical repulsive fractional potential fields in 3D environment	2
Galerkin method for time fractional semilinear equations	2
On the variable order fractional calculus of fractal interpolation functions	2
The similarity method and explicit solutions for the fractional space one-phase Stefan problems	2
A spectral approach to non-linear weakly singular fractional integro-differential equations	2
Multi-term fractional oscillation integro-differential equations	2
Approximation with continuous functions preserving fractal dimensions of the Riemann-Liouville operators of fractional calculus	2
Considerations regarding the accuracy of fractional numerical computations	2
Asymptotics of Fundamental Solutions for Time Fractional Equations with Convolution Kernels	2
On discrete tempered fractional calculus and its application	2
On differentiability of solutions of fractional differential equations with respect to initial data	2
Vallée-Poussin theorem for fractional functional differential equations	2
A fractional approach to study the pure-temporal Epidemic Type Aftershock Sequence (ETAS) process for earthquakes modeling	2
Exterior controllability properties for a fractional Moore–Gibson–Thompson equation	2
Some nonexistence results for space–time fractional Schrödinger equations without gauge invariance	2
Attractors of Caputo fractional differential equations with triangular vector fields	2
Dual Spaces of Anisotropic Variable Hardy–Lorentz Spaces and Their Applications	1
Sharp asymptotics in a fractional Sturm-Liouville problem	1
B-Spline Collocation Discretizations of Caputo and Riemann-Liouville Derivatives: A Matrix Comparison	1
Analysis of a fractional viscoelastic Euler-Bernoulli beam and identification of its piecewise continuous polynomial order	1
Properties of the multi-index special function $${\mathcal {W}}^{\left( \bar{\alpha },\bar{\nu }\right) }(z)$$	1
Porous functions–II	1
A variational theory for integral functionals involving finite-horizon fractional gradients	1
Limitations and applications in a fractional Barbalat’s Lemma	1
Numerical investigation of two models of nonlinear fractional reaction subdiffusion equations	1
Small order limit of fractional Dirichlet sublinear-type problems	1
Multivariable Fractional-Order PID Tuning by Iterative Non-Smooth Static-Dynamic H∞ Synthesis	1
Fractional Langevin Type Equations for White Noise Distributions	1
Skellam and time-changed variants of the generalized fractional counting process	1
General one-dimensional model of the time-fractional diffusion-wave equation in various geometries	1
Fractional Fractals	1
Integrability Properties of Integral Transforms Via Morrey Spaces	1
Anniversary of Prof. S.G. Samko, FC Events (FCAA–Volume 24–2–2021)	1
Delsarte equation for Caputo operator of fractional calculus	1
Riemann-Liouville derivatives of abstract functions and Sobolev spaces	1
A non-local semilinear eigenvalue problem	1
α-fractionally convex functions	1
Symmetry of solutions for asymptotically symmetric nonlocal parabolic equations	1
Reconstruction of pointwise sources in a time-fractional diffusion equation	1
Mixed stochastic heat equation with fractional Laplacian and gradient perturbation	1
Existence and uniqueness of a weak solution to fractional single-phase-lag heat equation	1
Kinetic Solutions for Nonlocal Stochastic Conservation Laws	1
Existence of an infinite system of fractional hybrid differential equations in a tempered sequence space	1
Continuous Dependence of Fuzzy Mild Solutions on Parameters for IVP of Fractional Fuzzy Evolution Equations	1
Entropy and alternative entropy functionals of fractional Gaussian noise as the functions of Hurst index	1
On the Asymptotics of Wright Functions of the Second Kind	1
Local and global conserved quantities involving generalized operators	1
Multi-parametric Le Roy function revisited	1
Optimal regional control for a class of semilinear time-fractional diffusion systems with distributed feedback	1
Local Existence and Non-Existence for a Fractional Reaction-Diffusion Equation in Lebesgue Spaces	1
Subordination principle and approximation of fractional resolvents and applications to fractional evolution equations	1
Lump solutions of the fractional Kadomtsev–Petviashvili equation	1
Asymptotics of the s-fractional Gaussian perimeter as $$s\rightarrow 0^+$$	1
The fractional stochastic heat equation driven by time-space white noise	1
Difference Between Riesz Derivative and Fractional Laplacian on the Proper Subset of ℝ	1
The Lambert function method in qualitative analysis of fractional delay differential equations	1
First order Plus Fractional Diffusive Delay Modeling: Interconnected Discrete Systems	1
The 2-Adic Derivatives and Fractal Dimension of Takagi-Like Function on 2-Series Field	1
Asymptotics of the Mittag-Leffler function $$E_a(z)$$ on the negative real axis when $$a \rightarrow 1$$	1