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 2020-05-01 to 2024-05-01.)

Article	Citations
Why Fractional Derivatives with Nonsingular Kernels Should Not Be Used	88
Operational Calculus for the General Fractional Derivative and Its Applications	71
Fractional Derivatives and the Fundamental Theorem of Fractional Calculus	43
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	29
ContribUtions on Artificial Potential Field Method for Effective Obstacle Avoidance	27
Degenerate Kirchhoff (p, q)–Fractional Systems with Critical Nonlinearities	26
Determination of the Order of Fractional Derivative for Subdiffusion Equations	23
A Cauchy problem for fractional evolution equations with Hilfer’s fractional derivative on semi-infinite interval	23
Convolution series and the generalized convolution Taylor formula	22
Towards a Unified theory of Fractional and Nonlocal Vector Calculus	21
On Representation Formulas for Solutions of Linear Differential Equations with Caputo Fractional Derivatives	21
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	20
Unified predictor–corrector method for fractional differential equations with general kernel functions	19
Box dimension of mixed Katugampola fractional integral of two-dimensional continuous functions	19
Operational Calculus for the Riemann–Liouville Fractional Derivative with Respect to a Function and its Applications	19
Fractional Euler numbers and generalized proportional fractional logistic differential equation	17
Fractional Derivatives and Cauchy Problem for Differential Equations of Fractional Order	17
Attractivity for Differential Equations of Fractional order and ψ-Hilfer Type	17
Well-Posedness for Weak and Strong Solutions of Non-Homogeneous Initial Boundary Value Problems for Fractional Diffusion Equations	16
Non-stationary zipper $$\alpha $$-fractal functions and associated fractal operator	15
Hölder regularity for non-autonomous fractional evolution equations	15
Optimal feedback control for a class of fractional evolution equations with history-dependent operators	15
The Bouncing Ball and the Grünwald-Letnikov Definition of Fractional Derivative	15

An Averaging Principle For Stochastic Differential Equations Of Fractional Order 0 < α < 1	14
Inverse Problem for a Multi-Term Fractional Differential Equation	13
Generalized Fractional Poisson Process and Related Stochastic Dynamics	13
Three Representations of the Fractional p-Laplacian: Semigroup, Extension and Balakrishnan Formulas	13
Fractional integral operators on Orlicz slice Hardy spaces	13
Uniqueness for an Inverse Source Problem of Determining a Space-Dependent Source in a Non-Autonomous Time-Fractional Diffusion Equation	13
Inverse Problems for Diffusion Equation with Fractional Dzherbashian-Nersesian Operator	13
Fractional-Order Susceptible-Infected Model: Definition and Applications to the Study of COVID-19 Main Protease	13
Analytical and dimensional properties of fractal interpolation functions on the Sierpiński gasket	13
Error Analysis of Nonlinear Time Fractional Mobile/Immobile Advection-Diffusion Equation with Weakly Singular Solutions	12
The Crank-Nicolson Type Compact Difference Schemes for a Loaded Time-Fractional Hallaire Equation	12
SHould I Stay Or Should I Go? Zero-Size Jumps in Random Walks for Lévy Flights	12
Convergence analysis of the time-stepping numerical methods for time-fractional nonlinear subdiffusion equations	12
Applications of Hilfer-Prabhakar Operator to Option Pricing Financial Model	11
Analysis of Fractional Integro-Differential Equations with Nonlocal Erdélyi-Kober Type Integral Boundary Conditions	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 fractional-order Lorenz-type systems: A review	11
Variational Methods to the p-Laplacian type Nonlinear Fractional Order Impulsive Differential Equations with Sturm-Liouville Boundary-Value Problem	11
Approximate inversion for Abel integral operators of variable exponent and applications to fractional Cauchy problems	10
Stability analysis of Hadamard and Caputo-Hadamard fractional nonlinear systems without and with delay	10
Recent Developments on the Realization of Fractance Device	10
The Green Function for a Class of Caputo Fractional Differential Equations with a Convection Term	9
Variational Approximation for Fractional Sturm–Liouville Problem	9
Cauchy Problem for General Time Fractional Diffusion Equation	9
Output Error MISO System Identification Using Fractional Models	9
RenoRmalization Group and Fractional Calculus Methods in a Complex World: A Review	9
Analysis of Solutions of Some Multi-Term Fractional Bessel Equations	8
The fractional variation and the precise representative of $$BV^{\alpha ,p}$$ functions	8
Determination of the Fractional Order in Semilinear Subdiffusion Equations	8
Subordination and memory dependent kinetics in diffusion and relaxation phenomena	8
Two High-Order Time Discretization Schemes for Subdiffusion Problems with Nonsmooth Data	8
An inverse problem of determining orders of systems of fractional pseudo-differential equations	7
Nontrivial Solutions of Non-Autonomous Dirichlet Fractional Discrete Problems	7
Fractional vector-valued nonuniform MRA and associated wavelet packets on $$L^2\big ({\mathbb {R}},{\mathbb {C}}^M\big )$$	7
Green’s Function for the Fractional KDV Equation on the Periodic Domain via Mittag-Leffler Function	7
Existence and Controllability Results for Hilfer Fractional Evolution Equations via Integral Contractors	7
Optimized fractional-order Butterworth filter design in complex F-plane	7
Upper and lower estimates for the separation of solutions to fractional differential equations	7
Asymptotic cycles in fractional maps of arbitrary positive orders	7
Exact solutions of fractional oscillation systems with pure delay	7
On a Method of Solution of Systems of Fractional Pseudo-Differential Equations	7
Multivariate Fractional Phase—Type Distributions	7
Multiple Positive Solutions for a Nonlocal Pde with Critical Sobolev-Hardy and Singular Nonlinearities Via Perturbation Method.	7
Initial-boundary value problems for multi-term time-fractional wave equations	6
Approximate controllability results for the Sobolev type fractional delay impulsive integrodifferential inclusions of order $${r} \in (1,2)$$ via sectorial operator	6
Subordination principle and Feynman-Kac formulae for generalized time-fractional evolution equations	6
Regularity Results for Nonlocal Evolution Venttsel’ Problems	6
Boundedness of fractional integrals on special John–Nirenberg–Campanato and Hardy-type spaces via congruent cubes	6
Two disjoint and infinite sets of solutions for a concave-convex critical fractional Laplacian equation	6

Wave Propagation Dynamics in a Fractional Zener Model with Stochastic Excitation	6
Short time coupled fractional fourier transform and the uncertainty principle	6
Some Properties of the Fractal Convolution of Functions	6
Fractional Integro-Differential Equations in Wiener Spaces	6
On the fractional Laplacian of variable order	6
Monte Carlo method for fractional-order differentiation extended to higher orders	6
Stability Analysis for Discrete Time Abstract Fractional Differential Equations	6
Two families of second-order fractional numerical formulas and applications to fractional differential equations	6
Duality Theory of Fractional Resolvents and Applications to Backward Fractional Control Systems	5
Implementation of Fractional Optimal Control Problems in Real-World Applications	5
(N + α)-Order low-pass and high-pass filter transfer functions for non-cascade implementations approximating butterworth response	5
Solution of Linear Fractional Order Systems with Variable Coefficients	5
Finite-approximate controllability of impulsive $$\psi -$$Caputo fractional evolution equations with nonlocal conditions	5
Exact solutions and Hyers-Ulam stability of fractional equations with double delays	5
Tempered Relaxation Equation and Related Generalized Stable Processes	5
Caputo delta weakly fractional difference equations	5
A fractional version of the recursive Tau method for solving a general class of Abel-Volterra integral equations systems	5
Optimal F-domain stabilization technique for reduction of commensurate fractional-order SISO systems	5
Multi-parametric Le Roy function	5
Prabhakar function of Le Roy type: a set of results in the complex plane	5
Determination of Time-Dependent Sources and Parameters of Nonlocal Diffusion and Wave Equations from Final Data	5
AsymptotIc Behavior of Solutions of Fractional Differential Equations with Hadamard Fractional Derivatives	5
Sliding methods for the higher order fractional laplacians	5
Global solutions of nonlinear fractional diffusion equations with time-singular sources and perturbed orders	4
Differentiation of integral Mittag-Leffler and integral Wright functions with respect to parameters	4
Stochastic solutions of generalized time-fractional evolution equations	4
On differentiability of solutions of fractional differential equations with respect to initial data	4
Simultaneous inversion for the fractional exponents in the space-time fractional diffusion equation $$\partial _t^\beta u = - {\left( { - \Delta } \right)^{\alpha /2}}u - {\left( { - \Delta } \right)^	4
On the Harmonic Extension Approach to Fractional Powers in Banach Spaces	4
Wright functions of the second kind and Whittaker functions	4
Maximum Principles and Applications for Fractional Differential Equations with Operators Involving Mittag-Leffler Function	4
Properties of the Set of Admissible “State Control” Pair for a Class of Fractional Semilinear Evolution Control Systems	4
Initial-boundary value problems for coupled systems of time-fractional diffusion equations	4
Multiple positive solutions for higher-order fractional integral boundary value problems with singularity on space variable	4
Fractional boundary value problems	4
Discrete Fractional Boundary Value Problems and Inequalities	4
Spectral analysis of multifractional LRD functional time series	4
Sequential generalized Riemann–Liouville derivatives based on distributional convolution	4
Variational methods for nonpositive mixed local–nonlocal operators	4
Computation of the inverse Mittag–Leffler function and its application to modeling ultraslow dynamics	4
The existence and averaging principle for Caputo fractional stochastic delay differential systems	4
Mkhitar Djrbashian and His Contribution to Fractional Calculus	4
Mixed order elliptic problems driven by a singularity, a Choquard type term and a discontinuous power nonlinearity with critical variable exponents	4
On mild solutions of the generalized nonlinear fractional pseudo-parabolic equation with a nonlocal condition	4
Anisotropic variable Campanato-type spaces and their Carleson measure characterizations	4
Semilinear Fractional Elliptic Problems with Mixed Dirichlet-Neumann Boundary Conditions	4
Sensitivity analysis for a fractional stochastic differential equation with $$S^{p}$$-weighted pseudo almost periodic coefficients and infinite delay	4
Monte Carlo Estimation of the Solution of Fractional Partial Differential Equations	4
Numerical scheme for Erdélyi–Kober fractional diffusion equation using Galerkin–Hermite method	4
Connections between nonlocal operators: from vector calculus identities to a fractional Helmholtz decomposition	4
Summability of Formal Solutions for a Family of Generalized Moment Integro-Differential Equations	4
Hölder regularity for the nonlinear stochastic time-fractional slow & fast diffusion equations on $${\mathbb {R}}^d$$	4
Impulse response of commensurate fractional-order systems: multiple complex poles	4
Approximation with continuous functions preserving fractal dimensions of the Riemann-Liouville operators of fractional calculus	4