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On Fractional Operators and Their Classifications
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1007/bf01171116openalex-snapshot
Some properties of fractional integrals. I.
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Some properties of fractional integrals. II
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Sur la représentation analytique d’une branche uniforme d’une fonction monogène: cinquième note
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A brief history and exposition of the fundamental theory of fractional calculus
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General Fractional Calculus, Evolution Equations, and Renewal Processes
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On the notion of fractional derivative and applications to the hysteresis phenomena
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Representations of acting processes and memory effects: General fractional derivative and its application to theory of heat conduction with finite wave speeds
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On fractional calculus with general analytic kernels
inferredcites →https://doi.org/10.1016/j.chaos.2018.07.033openalex-snapshot
Fractional derivatives with no-index law property: Application to chaos and statistics
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Mathematical analysis and numerical simulation for a smoking model with Atangana–Baleanu derivative
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On some new properties of fractional derivatives with Mittag-Leffler kernel
inferredcites →https://doi.org/10.1016/j.cnsns.2018.04.019openalex-snapshot
A new collection of real world applications of fractional calculus in science and engineering
inferredcites →https://doi.org/10.1016/j.cnsns.2018.07.035openalex-snapshot
Series representations for fractional-calculus operators involving generalised Mittag-Leffler functions
inferredcites →https://doi.org/10.1016/j.jcp.2014.04.024openalex-snapshot
Tempered fractional calculus
inferredcites →https://doi.org/10.1016/j.jcp.2014.07.019openalex-snapshot
What is a fractional derivative?
inferredcites →https://doi.org/10.1016/s0096-3003(02)00396-xopenalex-snapshot
Fractional calculus and some intermediate physical processes
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Versuch einer allgemeinen Auffassung der Integration und Differentiation. (1847.)
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Two-strain epidemic model involving fractional derivative with Mittag-Leffler kernel
inferredcites →https://doi.org/10.1080/10652460310001600717openalex-snapshot
Generalized mittag-leffler function and generalized fractional calculus operators
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A unified rheological model for cells and cellularised materials
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A general fractional differential equation associated with an integral operator with the H-function in the kernel
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Some Families of the Incomplete H-Functions and the Incomplete $$\overline H $$-Functions and Associated Integral Transforms and Operators of Fractional Calculus with Applications
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Leibniz Rule for Fractional Derivatives Generalized and an Application to Infinite Series
inferredcites →https://doi.org/10.1137/0501026openalex-snapshot
The Fractional Derivative of a Composite Function
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Applications of Fractional Calculus in Physics
inferredcites →https://doi.org/10.1186/s13662-017-1306-zopenalex-snapshot
On a new class of fractional operators
inferredcites →https://doi.org/10.1186/s13662-018-1612-0openalex-snapshot
A comparative study on generating function relations for generalized hypergeometric functions via generalized fractional operators
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Nonhomogeneous initial and boundary value problem for the Caputo-type fractional wave equation
inferredcites →https://doi.org/10.1515/9783110571622-003openalex-snapshot
Mathematical and physical interpretations of fractional derivatives and integrals
inferredcites →https://doi.org/10.1515/fca-2018-0003openalex-snapshot
Properties of the Caputo-Fabrizio fractional derivative and its distributional settings
inferredcites →https://doi.org/10.2298/fil1901245fopenalex-snapshot
On a new definition of fractional differintegrals with Mittag-Leffer kernel
inferredcites →https://doi.org/10.2298/tsci160111018aopenalex-snapshot
New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model
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Fractional Differential Equations
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The Craft of Fractional Modeling in Science and Engineering 2017
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Desiderata for Fractional Derivatives and Integrals
inferredcites →https://doi.org/10.3390/math7060485openalex-snapshot
Some New Fractional-Calculus Connections between Mittag–Leffler Functions
inferredcites →https://doi.org/10.3934/dcdsb.2019026openalex-snapshot
Well-posedness and numerical algorithm for the tempered fractional differential equations
inferredcites →https://doi.org/10.48550/arxiv.1501.00376openalex-snapshot
Well-posedness and numerical algorithm for the tempered fractional ordinary differential equations
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Incoming claims: where this work appears in other papers’ reference lists and arguments.
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inferred← citeshttps://doi.org/10.1186/s13662-019-2459-8openalex-snapshot
Existence and uniqueness of solutions for system of Hilfer–Hadamard sequential fractional differential equations with two point boundary conditions
inferred← citeshttps://doi.org/10.1186/s13662-020-02554-8openalex-snapshot
On the solution of two-dimensional fractional Black–Scholes equation for European put option
inferred← citeshttps://doi.org/10.1186/s13662-020-02638-5openalex-snapshot
Relations between fractional models with three-parameter Mittag-Leffler kernels
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A fractional derivative with two singular kernels and application to a heat conduction problem
inferred← citeshttps://doi.org/10.1186/s13662-020-03003-2openalex-snapshot
General conformable estimators with finite-time stability
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Modeling of pressure–volume controlled artificial respiration with local derivatives
inferred← citeshttps://doi.org/10.1186/s13662-020-2492-7openalex-snapshot
Stochastic resonance of fractional-order Langevin equation driven by periodic modulated noise with mass fluctuation
inferred← citeshttps://doi.org/10.1186/s13662-021-03270-7openalex-snapshot
Fractional calculus in the sky
inferred← citeshttps://doi.org/10.1186/s13662-021-03304-0openalex-snapshot
Analysis and applications of the proportional Caputo derivative
inferred← citeshttps://doi.org/10.1186/s13663-021-00696-2openalex-snapshot
Solving a well-posed fractional initial value problem by a complex approach
inferred← citeshttps://doi.org/10.11948/20220504openalex-snapshot
NUMERICAL TECHNIQUE BASED ON GENERALIZED LAGUERRE AND SHIFTED CHEBYSHEV POLYNOMIALS
inferred← citeshttps://doi.org/10.1216/rmj.2023.53.1337openalex-snapshot
CALCULUS OF VARIATIONS AND OPTIMAL CONTROL WITH GENERALIZED DERIVATIVE
inferred← citeshttps://doi.org/10.1515/dema-2022-0149openalex-snapshot
On Opial-type inequality for a generalized fractional integral operator
inferred← citeshttps://doi.org/10.1515/fca-2019-0079openalex-snapshot
A time-space Hausdorff derivative model for anomalous transport in porous media
inferred← citeshttps://doi.org/10.1515/fca-2020-0012openalex-snapshot
Comments on: “The Failure of Certain Fractional Calculus Operators in Two Physical Models” by M. Ortigueira, V. Martynyuk, M. Fedula and J.A.T. Machado
inferred← citeshttps://doi.org/10.1515/fca-2021-0023openalex-snapshot
Operational Calculus for the Riemann–Liouville Fractional Derivative with Respect to a Function and its Applications
inferred← citeshttps://doi.org/10.1515/phys-2020-0114openalex-snapshot
Some new extensions for fractional integral operator having exponential in the kernel and their applications in physical systems
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On some integral inequalities for $(h,m)$-convex functions in a generalized framework
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A Conformable Inverse Problem with Constant Delay
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On the generalized laplace transform and applications
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Delta Fractional Sturm--Liouville Problems: From Discrete to Continuous
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The novel investigation to Fornberg-Whitham equation via fractional natural transform decomposition method
inferred← citeshttps://doi.org/10.2298/fil2311659mopenalex-snapshot
Integral inequalities in fractional calculus with general analytic kernels
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Thermal analysis of magnetohydrodynamic viscous fluid with innovative fractional derivative
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Prabhakar fractional derivative and its applications in the transport phenomena containing nanoparticles
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Unsteady flow of Casson nanofluid through generalized Fourier's and Fick's law for heat and mass transfer
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A novel fractional study on free convection flow of Brinkmann hybrid nanofluid over an inclined plate
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On a generalization of the Wirtinger inequality and some its applications
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Dual Thermal Analysis of Fractional Convective Flow Through Aluminum Oxide and Titanium Dioxide Nanoparticles
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Uniqueness theorems for some classes of nonlinear fractional differential equations in the Riemann-Liouville sense
inferred← citeshttps://doi.org/10.32604/cmes.2023.025033openalex-snapshot
Fractional Order Modeling of Predicting COVID-19 with Isolation and Vaccination Strategies in Morocco
inferred← citeshttps://doi.org/10.32604/iasc.2022.020542openalex-snapshot
Computational Approach via Half-Sweep and Preconditioned AOR for Fractional Diffusion
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A generalized Bernoulli differential equation
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Some reflections on the problems and their role in the development of mathematics
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The Fractional Integral Inequalities Involving Kober and Saigo–Maeda Operators
inferred← citeshttps://doi.org/10.3389/fphy.2020.00072openalex-snapshot
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inferred← citeshttps://doi.org/10.3390/axioms10040283openalex-snapshot
Some New Post-Quantum Integral Inequalities Involving Twice (p, q)-Differentiable ψ-Preinvex Functions and Applications
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On a New Generalized Integral Operator and Certain Operating Properties
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High-Security Image Encryption Based on a Novel Simple Fractional-Order Memristive Chaotic System with a Single Unstable Equilibrium Point
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Modified Mittag-Leffler Functions with Applications in Complex Formulae for Fractional Calculus
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Electrical Circuits RC, LC, and RLC under Generalized Type Non-Local Singular Fractional Operator
inferred← citeshttps://doi.org/10.3390/fractalfract5030080openalex-snapshot
Fractional Integral Inequalities for Exponentially Nonconvex Functions and Their Applications
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Solutions of General Fractional-Order Differential Equations by Using the Spectral Tau Method
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Weighted Fractional Calculus: A General Class of Operators
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A Rigorous Analysis of Integro-Differential Operators with Non-Singular Kernels
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Fractional Calculus and Hypergeometric Functions in Complex Analysis
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inferred← citeshttps://doi.org/10.3390/fractalfract9020058openalex-snapshot
Regularity Results for Hybrid Proportional Operators on Hölder Spaces
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inferred← citeshttps://doi.org/10.3390/math11234772openalex-snapshot
Representation of Fractional Operators Using the Theory of Functional Connections
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inferred← citeshttps://doi.org/10.3390/math13162551openalex-snapshot
Fractional Order Analysis of Creep Characteristics of Sandstone with Multiscale Damage
inferred← citeshttps://doi.org/10.3390/math13182920openalex-snapshot
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inferred← citeshttps://doi.org/10.3390/math8030360openalex-snapshot
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Multi-Term Fractional Degenerate Evolution Equations and Optimal Control Problems
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Effective Method for Solving Different Types of Nonlinear Fractional Burgers’ Equations
inferred← citeshttps://doi.org/10.3390/math8060893openalex-snapshot
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inferred← citeshttps://doi.org/10.3390/math9172084openalex-snapshot
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inferred← citeshttps://doi.org/10.3390/quantum7020020openalex-snapshot
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inferred← citeshttps://doi.org/10.3390/sym12040626openalex-snapshot
Novel Fractional Operators with Three Orders and Power-Law, Exponential Decay and Mittag–Leffler Memories Involving the Truncated M-Derivative
inferred← citeshttps://doi.org/10.3390/sym14040739openalex-snapshot
Analytical Investigation of Fractional-Order Korteweg–De-Vries-Type Equations under Atangana–Baleanu–Caputo Operator: Modeling Nonlinear Waves in a Plasma and Fluid
inferred← citeshttps://doi.org/10.3390/sym14102168openalex-snapshot
Fractional View Analysis of Emden-Fowler Equations with the Help of Analytical Method
inferred← citeshttps://doi.org/10.3390/sym14122491openalex-snapshot
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inferred← citeshttps://doi.org/10.3390/sym15040862openalex-snapshot
Pre-Invexity and Fuzzy Fractional Integral Inequalities via Fuzzy Up and Down Relation
inferred← citeshttps://doi.org/10.3390/sym15081522openalex-snapshot
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inferred← citeshttps://doi.org/10.37376/ljst.v14i2.7209openalex-snapshot
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inferred← citeshttps://doi.org/10.37917/ijeee.17.1.14openalex-snapshot
New Fractional Order Chaotic System: Analysis, Synchronization, and it’s Application
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