Results 21 to 30 of about 283 (92)

A New Generalized Definition of Fractal–Fractional Derivative with Some Applications

Mathematical and Computational Applications
In this study, a new generalized fractal–fractional (FF) derivative is proposed. By applying this definition to some elementary functions, we show its compatibility with the results of the FF derivative in the Caputo sense with the power law.
Francisco Martínez, Mohammed K. A. Kaabar   +1 more
doaj   +1 more source

A Foundational Analysis of Local Kernel-Based Calculus

Axioms
We introduce the local kernel-based calculus, a unifying framework for local differential and integral operators based on an arbitrary positive continuous kernel function.
Pierros Ntelis
doaj   +1 more source

Non-Additivity and Additivity in General Fractional Calculus and Its Physical Interpretations

Fractal and Fractional
In this work, some properties of the general convolutional operators of general fractional calculus (GFC), which satisfy analogues of the fundamental theorems of calculus, are described. Two types of general fractional (GF) operators on a finite interval
Vasily E. Tarasov
doaj   +1 more source

General Fractional Economic Dynamics with Memory

Mathematics
For the first time, a self-consistent mathematical approach to describe economic processes with a general form of a memory function is proposed. In this approach, power-type memory is a special case of such general memory.
Vasily E. Tarasov
doaj   +1 more source

Third-Order Differential Subordination Results for Meromorphic Functions Associated with the Inverse of the Legendre Chi Function via the Mittag-Leffler Identity

Mathematics
In this paper, we derive novel results concerning third-order differential subordinations for meromorphic functions, utilizing a newly defined linear operator that involves the inverse of the Legendre chi function in conjunction with the Mittag-Leffler ...
Adel Salim Tayyah, Waggas Galib Atshan, Georgia Irina Oros   +2 more
doaj   +1 more source

New Findings of Gronwall–Bellman–Bihari Type Integral Inequalities with Applications to Fractional and Composite Nonlinear Systems

Mathematics
This paper is dedicated to the investigation of new generalizations of the classical Gronwall–Bellman–Bihari integral inequalities, which are fundamental tools in the qualitative and quantitative analysis of differential, integral, and integro ...
Liqiang Chen, Norazrizal Aswad Abdul Rahman   +1 more
doaj   +1 more source

Pseudo-Differential and Fractional Schrödinger Operators on Grand Variable Herz–Morrey–Hardy Spaces with Muckenhoupt Weights

Fractal and Fractional
Fractional differential operators equipped with classical and new memory kernels have emerged as indispensable tools for modeling systems with hereditary and non-local effects, offering a flexible framework that extends far beyond the classical integer ...
Waqar Afzal, Mujahid Abbas, Zareen A. Khan   +2 more
doaj   +1 more source

Stability Criteria for Nonlinear-Truncated V-Fractional-Order Derivative Systems with Applications to Synchronization. [PDF]

Entropy (Basel)
Yang W.
europepmc   +1 more source

Qualitative analysis and numerical simulation of ABC fractional impulsive differential systems with implicit nonlinear terms and integral boundary conditions. [PDF]

PLoS One
Sharif AA, Hamood M, Ghadle KP.
europepmc   +1 more source

Kicked General Fractional Lorenz-Type Equations: Exact Solutions and Multi-Dimensional Discrete Maps. [PDF]

Entropy (Basel)
Tarasov VE.
europepmc   +1 more source