Fractional Calculus and Applied Analysis

Article	Citations
Operational Calculus for the General Fractional Derivative and Its Applications	89
Completely Monotone Multinomial Mittag-Leffler Type Functions and Diffusion Equations with Multiple Time-Derivatives	35
ContribUtions on Artificial Potential Field Method for Effective Obstacle Avoidance	34
An efficient localized collocation solver for anomalous diffusion on surfaces	31
A Cauchy problem for fractional evolution equations with Hilfer’s fractional derivative on semi-infinite interval	30
Convolution series and the generalized convolution Taylor formula	30
Unified predictor–corrector method for fractional differential equations with general kernel functions	26
Determination of the Order of Fractional Derivative for Subdiffusion Equations	26
An Inverse Problem Approach to Determine Possible Memory Length of Fractional Differential Equations	23
Operational Calculus for the Riemann–Liouville Fractional Derivative with Respect to a Function and its Applications	23
Fractional Euler numbers and generalized proportional fractional logistic differential equation	22
Towards a Unified theory of Fractional and Nonlocal Vector Calculus	22
Box dimension of mixed Katugampola fractional integral of two-dimensional continuous functions	22
Optimal feedback control for a class of fractional evolution equations with history-dependent operators	21
A Survey on Numerical Methods for Spectral Space-Fractional Diffusion Problems	21
Non-stationary zipper $$\alpha $$-fractal functions and associated fractal operator	19
Fractional integral operators on Orlicz slice Hardy spaces	19
Three Representations of the Fractional p-Laplacian: Semigroup, Extension and Balakrishnan Formulas	17
Well-Posedness for Weak and Strong Solutions of Non-Homogeneous Initial Boundary Value Problems for Fractional Diffusion Equations	17
The Bouncing Ball and the Grünwald-Letnikov Definition of Fractional Derivative	17
Fractional Derivatives and Cauchy Problem for Differential Equations of Fractional Order	17
Hölder regularity for non-autonomous fractional evolution equations	16
SHould I Stay Or Should I Go? Zero-Size Jumps in Random Walks for Lévy Flights	16
Stability analysis of Hadamard and Caputo-Hadamard fractional nonlinear systems without and with delay	15
Convergence analysis of the time-stepping numerical methods for time-fractional nonlinear subdiffusion equations	15

Error Analysis of Nonlinear Time Fractional Mobile/Immobile Advection-Diffusion Equation with Weakly Singular Solutions	14
Characterizations of Variable Martingale Hardy Spaces Via Maximal Functions	14
The Crank-Nicolson Type Compact Difference Schemes for a Loaded Time-Fractional Hallaire Equation	14
Analytical and dimensional properties of fractal interpolation functions on the Sierpiński gasket	14
Subordination and memory dependent kinetics in diffusion and relaxation phenomena	14
Inverse Problems for Diffusion Equation with Fractional Dzherbashian-Nersesian Operator	14
Uniqueness for an Inverse Source Problem of Determining a Space-Dependent Source in a Non-Autonomous Time-Fractional Diffusion Equation	13
Variational Methods to the p-Laplacian type Nonlinear Fractional Order Impulsive Differential Equations with Sturm-Liouville Boundary-Value Problem	13
Recent Developments on the Realization of Fractance Device	12
The fractional-order Lorenz-type systems: A review	12
Monte Carlo method for fractional-order differentiation extended to higher orders	11
Exact Stability and Instability Regions for Two-Dimensional Linear Autonomous Multi-Order Systems of Fractional-Order Differential Equations	11
Approximate inversion for Abel integral operators of variable exponent and applications to fractional Cauchy problems	11
Existence and Controllability Results for Hilfer Fractional Evolution Equations via Integral Contractors	10
RenoRmalization Group and Fractional Calculus Methods in a Complex World: A Review	10
Output Error MISO System Identification Using Fractional Models	10
Exact solutions of fractional oscillation systems with pure delay	10
Upper and lower estimates for the separation of solutions to fractional differential equations	9
Analysis of Solutions of Some Multi-Term Fractional Bessel Equations	9
Approximation with continuous functions preserving fractal dimensions of the Riemann-Liouville operators of fractional calculus	9
Lyapunov stability theorems for $$\psi $$-Caputo derivative systems	9
Approximate controllability results for the Sobolev type fractional delay impulsive integrodifferential inclusions of order $${r} \in (1,2)$$ via sectorial operator	9
An inverse problem of determining orders of systems of fractional pseudo-differential equations	8
On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications	8
Finite-approximate controllability of impulsive $$\psi -$$Caputo fractional evolution equations with nonlocal conditions	8
Optimized fractional-order Butterworth filter design in complex F-plane	8
A new Bihari inequality and initial value problems of first order fractional differential equations	8
Green’s Function for the Fractional KDV Equation on the Periodic Domain via Mittag-Leffler Function	8
On a Method of Solution of Systems of Fractional Pseudo-Differential Equations	8
The fractional variation and the precise representative of $$BV^{\alpha ,p}$$ functions	8
Asymptotic cycles in fractional maps of arbitrary positive orders	8
Subordination principle and Feynman-Kac formulae for generalized time-fractional evolution equations	7
Fractional vector-valued nonuniform MRA and associated wavelet packets on $$L^2\big ({\mathbb {R}},{\mathbb {C}}^M\big )$$	7
Mellin definition of the fractional Laplacian	7
On approximate controllability of multi-term time fractional measure differential equations with nonlocal conditions	7
Numerical investigation of generalized tempered-type integrodifferential equations with respect to another function	7
Mixed order elliptic problems driven by a singularity, a Choquard type term and a discontinuous power nonlinearity with critical variable exponents	7
Two disjoint and infinite sets of solutions for a concave-convex critical fractional Laplacian equation	7
Connections between nonlocal operators: from vector calculus identities to a fractional Helmholtz decomposition	7
Implementation of Fractional Optimal Control Problems in Real-World Applications	7
Boundedness of fractional integrals on special John–Nirenberg–Campanato and Hardy-type spaces via congruent cubes	7
On the fractional Laplacian of variable order	7
Numerical scheme for Erdélyi–Kober fractional diffusion equation using Galerkin–Hermite method	6
Variational methods for nonpositive mixed local–nonlocal operators	6
Mkhitar Djrbashian and His Contribution to Fractional Calculus	6
Some Properties of the Fractal Convolution of Functions	6
On mild solutions of the generalized nonlinear fractional pseudo-parabolic equation with a nonlocal condition	6
AsymptotIc Behavior of Solutions of Fractional Differential Equations with Hadamard Fractional Derivatives	6
Determination of Time-Dependent Sources and Parameters of Nonlocal Diffusion and Wave Equations from Final Data	6
Sliding methods for the higher order fractional laplacians	6

Short time coupled fractional fourier transform and the uncertainty principle	6
Prabhakar function of Le Roy type: a set of results in the complex plane	6
Two families of second-order fractional numerical formulas and applications to fractional differential equations	6
Initial-boundary value problems for multi-term time-fractional wave equations	6
Fractional boundary value problems	6
Wave Propagation Dynamics in a Fractional Zener Model with Stochastic Excitation	6
Stability Analysis for Discrete Time Abstract Fractional Differential Equations	6
Multi-parametric Le Roy function	6
(N + α)-Order low-pass and high-pass filter transfer functions for non-cascade implementations approximating butterworth response	6
Global solutions of nonlinear fractional diffusion equations with time-singular sources and perturbed orders	6
Existence for a class of time-fractional evolutionary equations with applications involving weakly continuous operator	6
Caputo delta weakly fractional difference equations	6
Duality Theory of Fractional Resolvents and Applications to Backward Fractional Control Systems	5
Stability analysis of fractional differential equations with the short-term memory property	5
Monte Carlo method for fractional-order differentiation	5
A fractional version of the recursive Tau method for solving a general class of Abel-Volterra integral equations systems	5
Monte Carlo Estimation of the Solution of Fractional Partial Differential Equations	5
On differentiability of solutions of fractional differential equations with respect to initial data	5
Exact solutions and Hyers-Ulam stability of fractional equations with double delays	5
Attractors of Caputo fractional differential equations with triangular vector fields	5
Impulse response of commensurate fractional-order systems: multiple complex poles	5
Initial-boundary value problems for coupled systems of time-fractional diffusion equations	5
System of fractional boundary value problems at resonance	5
A variational theory for integral functionals involving finite-horizon fractional gradients	5
Sequential generalized Riemann–Liouville derivatives based on distributional convolution	5
On Fractional Heat Equation	5
Summability of Formal Solutions for a Family of Generalized Moment Integro-Differential Equations	5
Fractional models for analysis of economic risks	5
Multiple positive solutions for higher-order fractional integral boundary value problems with singularity on space variable	5
Stochastic solutions of generalized time-fractional evolution equations	5
Optimal F-domain stabilization technique for reduction of commensurate fractional-order SISO systems	5
Vallée-Poussin theorem for fractional functional differential equations	4
A fractional approach to study the pure-temporal Epidemic Type Aftershock Sequence (ETAS) process for earthquakes modeling	4
Some estimates for $$p$$-adic fractional integral operator and its commutators on $$p$$-adic Herz spaces with rough kernels	4
Computation of the inverse Mittag–Leffler function and its application to modeling ultraslow dynamics	4
Weighted estimates for operators of fractional integration of variable order in generalized variable Hölder spaces	4
Controllability and observability of linear time-varying fractional systems	4
Maximum Principles and Applications for Fractional Differential Equations with Operators Involving Mittag-Leffler Function	4
Existence of an infinite system of fractional hybrid differential equations in a tempered sequence space	4
Dual Spaces of Anisotropic Variable Hardy–Lorentz Spaces and Their Applications	4
Anisotropic variable Campanato-type spaces and their Carleson measure characterizations	4
Subordination principle and approximation of fractional resolvents and applications to fractional evolution equations	4
Fractional Diffusion-Wave Equations: Hidden Regularity for Weak Solutions	4
Explicit Representation of Discrete Fractional Resolvent Families in Banach Spaces	4
Weighted Fractional Hardy Operators and their Commutators on Generalized Morrey Spaces over Quasi-Metric Measure Spaces	4
Wright functions of the second kind and Whittaker functions	4
Solvability of an infinite system of Langevin fractional differential equations in a new tempered sequence space	4
Properties of the Set of Admissible “State Control” Pair for a Class of Fractional Semilinear Evolution Control Systems	4
Existence and uniqueness of a weak solution to fractional single-phase-lag heat equation	4
Pricing Vulnerable Options in Fractional Brownian Markets: a Partial Differential Equations Approach	4
Differentiation of integral Mittag-Leffler and integral Wright functions with respect to parameters	4
Discrete Fractional Boundary Value Problems and Inequalities	4
Discrete fractional distributed Halanay inequality and applications in discrete fractional order neural network systems	4
Spectral analysis of multifractional LRD functional time series	4
A Fractional Analysis in Higher Dimensions for the Sturm-Liouville Problem	4
Asymptotic profile for a two-terms time fractional diffusion problem	4
Müntz sturm-liouville problems: Theory and numerical experiments	4
Hölder regularity for the nonlinear stochastic time-fractional slow & fast diffusion equations on $${\mathbb {R}}^d$$	4
The existence and averaging principle for Caputo fractional stochastic delay differential systems	4
Dynamical repulsive fractional potential fields in 3D environment	4
Analytical solutions for fractional partial delay differential-algebraic equations with Dirichlet boundary conditions defined on a finite domain	4
Asymptotic behaviour of solutions to non-commensurate fractional-order planar systems	4
Simultaneous inversion for the fractional exponents in the space-time fractional diffusion equation $$\partial _t^\beta u = - {\left( { - \Delta } \right)^{\alpha /2}}u - {\left( { - \Delta } \right)^	4
Sensitivity analysis for a fractional stochastic differential equation with $$S^{p}$$-weighted pseudo almost periodic coefficients and infinite delay	4
Extremal mild solutions to Hilfer evolution equations with non-instantaneous impulses and nonlocal conditions	3
Filter Regularization Method for a Nonlinear Riesz-Feller Space-Fractional Backward Diffusion Problem with Temporally Dependent Thermal Conductivity	3
Cauchy problem for non-autonomous fractional evolution equations	3
Fractional integral operator and its commutator on generalized Morrey spaces associated with ball Banach function spaces	3
New fractional maximal operators in the theory of martingale Hardy and Lebesgue spaces with variable exponents	3
On the Decomposition of Solutions: From Fractional Diffusion to Fractional Laplacian	3
Self-Similar Cauchy Problems and Generalized Mittag-Leffler Functions	3
Wind turbulence modeling for real-time simulation	3
Fractional differential equations of Bagley-Torvik and Langevin type	3
Robust Fractional-Order Perfect Control for Non-Full Rank Plants Described in the Grünwald-Letnikov IMC Framework	3
A non-local semilinear eigenvalue problem	3
A Strong Maximum Principle for the Fractional Laplace Equation with Mixed Boundary Condition	3
On the Green Function of the Killed Fractional Laplacian on the Periodic Domain	3
Existence of Solutions for the Semilinear Abstract Cauchy Problem of Fractional Order	3
The Rate of Convergence on Fractional Power Dissipative Operator on Compact Manifolds	3
Solvability of infinite systems of fractional differential equations in the double sequence space $$ 2^c(\triangle )$$	3

Bounded Solutions of Second Order of Accuracy Difference Schemes for Semilinear Fractional Schrödinger Equations	3
Nonlinear convolution integro-differential equation with variable coefficient	3
Stability analysis of a second-order difference scheme for the time-fractional mixed sub-diffusion and diffusion-wave equation	3
Multi-parametric Le Roy function revisited	3
Difference Between Riesz Derivative and Fractional Laplacian on the Proper Subset of ℝ	3
A class of Hilfer fractional differential evolution hemivariational inequalities with history-dependent operators	3
Fractional characteristic functions, and a fractional calculus approach for moments of random variables	3
Efficient spectral collocation method for fractional differential equation with Caputo-Hadamard derivative	3
On solvability for a class of nonlinear systems of differential equations with the Caputo fractional derivative	3
A novel approach to stability analysis of a wide class of irrational linear systems	3
Robust model predictive control for fractional-order descriptor systems with uncertainty	3
Galerkin method for time fractional semilinear equations	3
An elementary inequality for dissipative Caputo fractional differential equations	3
Final value problem for Rayleigh-Stokes type equations involving weak-valued nonlinearities	3
The similarity method and explicit solutions for the fractional space one-phase Stefan problems	3
Representations of solutions of systems of time-fractional pseudo-differential equations	3
Delsarte equation for Caputo operator of fractional calculus	3
Construction and analysis of series solutions for fractional quasi-Bessel equations	3
A Boundary Value Problem for a Partial Differential Equation with Fractional Derivative	3
On discrete tempered fractional calculus and its application	3
Skellam and time-changed variants of the generalized fractional counting process	2
Approximation results in Sobolev and fractional Sobolev spaces by sampling Kantorovich operators	2
Existence of positive solutions for fractional delayed evolution equations of order $$\gamma \in (1,2)$$ via measure of non-compactness	2
Partially explicit time discretization for time fractional diffusion equation	2
Entropy and alternative entropy functionals of fractional Gaussian noise as the functions of Hurst index	2
On a Solution of a Fractional Hyper-Bessel Differential Equation by Means of a Multi-Index Special Function	2
Orlicz-Lorentz-Karamata Hardy martingale spaces: inequalities and fractional integral operators	2
Trace regularity for biharmonic evolution equations with Caputo derivatives	2
Multi-term fractional oscillation integro-differential equations	2
An eigenvalue problem in fractional h-discrete calculus	2
Asymptotically autonomous dynamics for fractional subcritical nonclassical diffusion equations driven by nonlinear colored noise	2
Method of separation of variables and exact solution of time fractional nonlinear partial differential and differential-difference equations	2
Some nonexistence results for space–time fractional Schrödinger equations without gauge invariance	2
On approximate controllability of semi-linear neutral integro-differential evolution systems with state-dependent nonlocal conditions	2
Reachability of time-varying fractional dynamical systems with Riemann-Liouville fractional derivative	2
Existence and asymptotic behavior of square-mean S-asymptotically periodic solutions for fractional stochastic evolution equation with delay	2
Bounds for mixing times for finite semi-Markov processes with heavy-tail jump distribution	2
Reconstruction of pointwise sources in a time-fractional diffusion equation	2
On some even-sequential fractional boundary-value problems	2
Qualitative properties of solutions to a nonlinear time-space fractional diffusion equation	2
Continuous Dependence of Fuzzy Mild Solutions on Parameters for IVP of Fractional Fuzzy Evolution Equations	2
Exterior controllability properties for a fractional Moore–Gibson–Thompson equation	2
On the Asymptotics of Wright Functions of the Second Kind	2
Optimal approximation of analog PID controllers of complex fractional-order	2
Sharp asymptotics in a fractional Sturm-Liouville problem	2
Fractional Jacobi-Dunkl transform: properties and application	2
Global attractivity for fractional differential equations of Riemann-Liouville type	2
Multidimensional van der Corput-Type Estimates Involving Mittag-Leffler Functions	2
Inverse problem of determining the order of the fractional derivative in the Rayleigh-Stokes equation	2
A spectral approach to non-linear weakly singular fractional integro-differential equations	2
Considerations regarding the accuracy of fractional numerical computations	2
Analysis of a fractional viscoelastic Euler-Bernoulli beam and identification of its piecewise continuous polynomial order	2
RETRACTED ARTICLE: Averaging principle for stochastic Caputo fractional differential equations with non-Lipschitz condition	2
Multi-term fractional integro-differential equations in power growth function spaces	2
Limitations and applications in a fractional Barbalat’s Lemma	2
Symmetry and monotonicity of positive solutions for Choquard equations involving a generalized tempered fractional p-Laplacian in $${\mathbb {R}}^{n}$$	2
On the variable order fractional calculus of fractal interpolation functions	2
On the Rothe-Galerkin spectral discretization for a class of variable fractional-order nonlinear wave equations	2
Searching for Sonin kernels	2
Existence and multiplicity of solutions to magnetic Kirchhoff equations in Orlicz-Sobolev spaces	2
Asymptotics of the Mittag-Leffler function $$E_a(z)$$ on the negative real axis when $$a \rightarrow 1$$	2
Stochastic solutions for time-fractional heat equations with complex spatial variables	2
Averaging Theory for Fractional Differential Equations	2
Riesz Potentials and Orthogonal Radon Transforms on Affine Grassmannians	2
Numerical conservation laws of time fractional diffusion PDEs	2
Two-weighted estimates for p-adic Riesz potential and its commutators on Morrey–Herz spaces	2
Kinetic Solutions for Nonlocal Stochastic Conservation Laws	2
Mixed stochastic heat equation with fractional Laplacian and gradient perturbation	2
Some boundedness results for Riemann-Liouville tempered fractional integrals	2
Existence of Local Solutions for Fractional Difference Equations with Left Focal Boundary Conditions	2
Superlinear solutions of sublinear fractional differential equations and regular variation	2
Queuing models with Mittag-Leffler inter-event times	2