Results 71 to 80 of about 291,483 (125)

ON GENERALIZED FRACTIONAL INTEGRALS AND DERIVATIVES

, 2011
In this paper we present a generalization to two existing fractional integrals and derivatives, namely, the Riemann-Liouville and Hadamard fractional operators.
Katugampola, Don Udita Nalin
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Incremental parameterized-kernel fractional operators: theory, novel Banach spaces, and machine learning applications

Ain Shams Engineering Journal
This paper presents a new class of Incremental Parameterized–Kernel (IPK) fractional derivative and integral operators that improve modeling of complex dynamical systems.
Tahir Ullah Khan, Christine Markarian
doaj   +1 more source

Optimal control of fractional systems: a diffusive formulation [PDF]

, 2010
Optimal control of fractional linear systems on a finite horizon can be classically formulated using the adjoint system. But the adjoint of a causal fractional integral or derivative operator happens to be an anti-causal operator: hence, the adjoint ...
Matignon, Denis
core  

Diffusive representations for fractional Laplacian: systems theory framework and numerical issues [PDF]

, 2009
Bridging the gap between an abstract definition of pseudo-differential operators, such as (-\Delta)^{\gamma} for - 1/2 < \gamma < 1/2, and a concrete way to represent them has proved difficult; deriving stable numerical schemes for such operators is not ...
Matignon, Denis
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Symmetrical Solutions for Non-Local Fractional Integro-Differential Equations via Caputo–Katugampola Derivatives

, 2023
Fractional calculus, which deals with the concept of fractional derivatives and integrals, has become an important area of research, due to its ability to capture memory effects and non-local behavior in the modeling of real-world phenomena. In this work,
Ali Hasan Ali, Khalil S. Al-Ghafri, Al-Ghafri, Khalil S., Iambor, Loredana Florentina, Saleh S. Redhwan, Alabdala, Awad T., Awad T. Alabdala, Loredana Florentina Iambor, Redhwan, Saleh S., Bazighifan, Omar, Omar Bazighifan, Ali, Ali Hasan   +11 more
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Novel Grüss-Type and Related Integral Inequalities via the Cotangent Fractional Integral with Respect to Another Function

Fractal and Fractional
This article investigates new classes of integral inequalities within the framework of a recently introduced fractional operator: the cotangent fractional integral with respect to a rising function (RAF) ℵ. The cornerstone of this study is the derivation
Ibtehal Alazman, Lakhlifa Sadek, Ahmad Shafee, Khalid Aldawsari   +3 more
doaj   +1 more source

ON MILNE-TYPE INEQUALITIES VIA KATUGAMPOLA FRACTIONAL MULTIPLICATIVE INTEGRALS

This work focuses on the study of Milne’s inequality in the framework of Katugampola fractional multiplicative integrals, inspired by recent progress in non-Newtonian fractional calculus.
Bin-Mohsin, Bandar, Achachera, Khalid, Xu, Hongyan, BUDAK, HÜSEYİN, LAKHDARI, Abdelghani   +4 more
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New Result for the Analysis of Katugampola Fractional-Order Systems—Application to Identification Problems

, 2022
In the last few years, a new class of fractional-order (FO) systems, known as Katugampola FO systems, has been introduced. This class is noteworthy to investigate, as it presents a generalization of the well-known Caputo fractional-order systems. In this
Omar Naifar, Omar Kahouli, Abdellatif Ben Makhlouf, Assaad Jmal, Abdelhameed M. Nagy   +4 more
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Fractional-order boundary value problems with Katugampola fractional integral conditions

, 2018
In this paper, we study existence (uniqueness) of solutions for nonlinear fractional differential equations with Katugampola fractional integral conditions.
Sedef Emin, Nazim I. Mahmudov
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The general Caputo–Katugampola fractional derivative and numerical approach for solving the fractional differential equations

In this manuscript, we present the general fractional derivative (FD) along with its fractional integral (FI), specifically the ψ-Caputo–Katugampola fractional derivative (ψ-CKFD).
Lakhlifa Sadek, Sahar Ahmed ldris, Fahd Jarad   +2 more
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