OOIR: Observatory of International Research

Papers

(The TQCC of Fractional Calculus and Applied Analysis is 4. The table below lists those papers that are above that threshold based on CrossRef citation counts [max. 250 papers]. The publications cover those that have been published in the past four years, i.e., from 2020-10-01 to 2024-10-01.)

Article	Citations
Operational Calculus for the General Fractional Derivative and Its Applications	83
ContribUtions on Artificial Potential Field Method for Effective Obstacle Avoidance	34
Completely Monotone Multinomial Mittag-Leffler Type Functions and Diffusion Equations with Multiple Time-Derivatives	33
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
Determination of the Order of Fractional Derivative for Subdiffusion Equations	26
Unified predictor–corrector method for fractional differential equations with general kernel functions	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
Box dimension of mixed Katugampola fractional integral of two-dimensional continuous functions	22
Fractional Euler numbers and generalized proportional fractional logistic differential equation	22
Towards a Unified theory of Fractional and Nonlocal Vector Calculus	22
A Survey on Numerical Methods for Spectral Space-Fractional Diffusion Problems	21
Optimal feedback control for a class of fractional evolution equations with history-dependent operators	20
Fractional integral operators on Orlicz slice Hardy spaces	19
Non-stationary zipper $$\alpha $$-fractal functions and associated fractal operator	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
Convergence analysis of the time-stepping numerical methods for time-fractional nonlinear subdiffusion equations	15
Subordination and memory dependent kinetics in diffusion and relaxation phenomena	14

Inverse Problems for Diffusion Equation with Fractional Dzherbashian-Nersesian Operator	14
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
Variational Methods to the p-Laplacian type Nonlinear Fractional Order Impulsive Differential Equations with Sturm-Liouville Boundary-Value Problem	13
Uniqueness for an Inverse Source Problem of Determining a Space-Dependent Source in a Non-Autonomous Time-Fractional Diffusion Equation	13
Stability analysis of Hadamard and Caputo-Hadamard fractional nonlinear systems without and with delay	13
Analysis of Fractional Integro-Differential Equations with Nonlocal Erdélyi-Kober Type Integral Boundary Conditions	12
The fractional-order Lorenz-type systems: A review	12
Recent Developments on the Realization of Fractance Device	12
Two High-Order Time Discretization Schemes for Subdiffusion Problems with Nonsmooth Data	11
Exact Stability and Instability Regions for Two-Dimensional Linear Autonomous Multi-Order Systems of Fractional-Order Differential Equations	11
Cauchy Problem for General Time Fractional Diffusion Equation	11
Approximate inversion for Abel integral operators of variable exponent and applications to fractional Cauchy problems	11
Exact solutions of fractional oscillation systems with pure delay	10
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
Approximate controllability results for the Sobolev type fractional delay impulsive integrodifferential inclusions of order $${r} \in (1,2)$$ via sectorial operator	10
Analysis of Solutions of Some Multi-Term Fractional Bessel Equations	9
Monte Carlo method for fractional-order differentiation extended to higher orders	9
Upper and lower estimates for the separation of solutions to fractional differential equations	9
Approximation with continuous functions preserving fractal dimensions of the Riemann-Liouville operators of fractional calculus	9
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
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
Connections between nonlocal operators: from vector calculus identities to a fractional Helmholtz decomposition	7
Tempered Relaxation Equation and Related Generalized Stable Processes	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
Subordination principle and Feynman-Kac formulae for generalized time-fractional evolution equations	7
Lyapunov stability theorems for $$\psi $$-Caputo derivative systems	7
Multivariate Fractional Phase—Type Distributions	7
On approximate controllability of multi-term time fractional measure differential equations with nonlocal conditions	7
Implementation of Fractional Optimal Control Problems in Real-World Applications	7
Fractional vector-valued nonuniform MRA and associated wavelet packets on $$L^2\big ({\mathbb {R}},{\mathbb {C}}^M\big )$$	7
Two disjoint and infinite sets of solutions for a concave-convex critical fractional Laplacian equation	7
AsymptotIc Behavior of Solutions of Fractional Differential Equations with Hadamard Fractional Derivatives	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
Prabhakar function of Le Roy type: a set of results in the complex plane	6
Short time coupled fractional fourier transform and the uncertainty principle	6

Fractional Integro-Differential Equations in Wiener Spaces	6
Mellin definition of the fractional Laplacian	6
On mild solutions of the generalized nonlinear fractional pseudo-parabolic equation with a nonlocal condition	6
Caputo delta weakly fractional difference equations	6
Numerical scheme for Erdélyi–Kober fractional diffusion equation using Galerkin–Hermite method	6
Multi-parametric Le Roy function	6
Stability Analysis for Discrete Time Abstract Fractional Differential Equations	6
(N + α)-Order low-pass and high-pass filter transfer functions for non-cascade implementations approximating butterworth response	6
Two families of second-order fractional numerical formulas and applications to fractional differential equations	6
Existence for a class of time-fractional evolutionary equations with applications involving weakly continuous operator	6
Global solutions of nonlinear fractional diffusion equations with time-singular sources and perturbed orders	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
Mkhitar Djrbashian and His Contribution to Fractional Calculus	6
Variational methods for nonpositive mixed local–nonlocal operators	6
Some Properties of the Fractal Convolution of Functions	6
Duality Theory of Fractional Resolvents and Applications to Backward Fractional Control Systems	5
Mixed order elliptic problems driven by a singularity, a Choquard type term and a discontinuous power nonlinearity with critical variable exponents	5
Impulse response of commensurate fractional-order systems: multiple complex poles	5
A fractional version of the recursive Tau method for solving a general class of Abel-Volterra integral equations systems	5
System of fractional boundary value problems at resonance	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
On Fractional Heat Equation	5
Attractors of Caputo fractional differential equations with triangular vector fields	5
Stability analysis of fractional differential equations with the short-term memory property	5
Fractional models for analysis of economic risks	5
Initial-boundary value problems for coupled systems of time-fractional diffusion equations	5
Stochastic solutions of generalized time-fractional evolution equations	5
Sequential generalized Riemann–Liouville derivatives based on distributional convolution	5
Exact solutions and Hyers-Ulam stability of fractional equations with double delays	5
Summability of Formal Solutions for a Family of Generalized Moment Integro-Differential Equations	5
Regularity Results for Nonlocal Evolution Venttsel’ Problems	5
Monte Carlo method for fractional-order differentiation	5
Multiple positive solutions for higher-order fractional integral boundary value problems with singularity on space variable	5
A variational theory for integral functionals involving finite-horizon fractional gradients	5
Optimal F-domain stabilization technique for reduction of commensurate fractional-order SISO systems	5
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}$$-weighted pseudo almost periodic coefficients and infinite delay	4
Explicit Representation of Discrete Fractional Resolvent Families in Banach Spaces	4
A fractional approach to study the pure-temporal Epidemic Type Aftershock Sequence (ETAS) process for earthquakes modeling	4
Weighted Fractional Hardy Operators and their Commutators on Generalized Morrey Spaces over Quasi-Metric Measure Spaces	4
Computation of the inverse Mittag–Leffler function and its application to modeling ultraslow dynamics	4
Müntz sturm-liouville problems: Theory and numerical experiments	4
Hölder regularity for the nonlinear stochastic time-fractional slow & fast diffusion equations on $${\mathbb {R}}^d$$	4
Maximum Principles and Applications for Fractional Differential Equations with Operators Involving Mittag-Leffler Function	4
Existence of an infinite system of fractional hybrid differential equations in a tempered sequence space	4
Dual Spaces of Anisotropic Variable Hardy–Lorentz Spaces and Their Applications	4
Anisotropic variable Campanato-type spaces and their Carleson measure characterizations	4
Subordination principle and approximation of fractional resolvents and applications to fractional evolution equations	4
Fractional Diffusion-Wave Equations: Hidden Regularity for Weak Solutions	4
A Fractional Analysis in Higher Dimensions for the Sturm-Liouville Problem	4
Asymptotic profile for a two-terms time fractional diffusion problem	4
Wright functions of the second kind and Whittaker functions	4
Weighted estimates for operators of fractional integration of variable order in generalized variable Hölder spaces	4
Properties of the Set of Admissible “State Control” Pair for a Class of Fractional Semilinear Evolution Control Systems	4
Existence and uniqueness of a weak solution to fractional single-phase-lag heat equation	4
Analytical solutions for fractional partial delay differential-algebraic equations with Dirichlet boundary conditions defined on a finite domain	4
Differentiation of integral Mittag-Leffler and integral Wright functions with respect to parameters	4
Discrete Fractional Boundary Value Problems and Inequalities	4
Discrete fractional distributed Halanay inequality and applications in discrete fractional order neural network systems	4
Vallée-Poussin theorem for fractional functional differential equations	4
Spectral analysis of multifractional LRD functional time series	4
Some estimates for $$p$$-adic fractional integral operator and its commutators on $$p$$-adic Herz spaces with rough kernels	4
Numerical investigation of generalized tempered-type integrodifferential equations with respect to another function	4
Controllability and observability of linear time-varying fractional systems	4
Solvability of an infinite system of Langevin fractional differential equations in a new tempered sequence space	4
The existence and averaging principle for Caputo fractional stochastic delay differential systems	4
Dynamical repulsive fractional potential fields in 3D environment	4
Pricing Vulnerable Options in Fractional Brownian Markets: a Partial Differential Equations Approach	4
Asymptotic behaviour of solutions to non-commensurate fractional-order planar systems	4