On Weighted Fractional Calculus With Respect to Functions
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DOI: 10.1002/mma.10626
Abstract: This paper aims to further explore the existing theory of weighted fractional operators with respect to functions. This theory extends some fundamental results of classical Riemann–Liouville and Caputo fractional derivatives to their weighted counterparts involving… read more here.
Keywords: respect functions; weighted fractional; fractional calculus; calculus respect ... See more keywords
An Extensive Study of Weighted Hilfer Fractional Calculus With Respect to Functions
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DOI: 10.1002/mma.70158
Abstract: This research contributes to the field of fractional calculus in theoretical sense. We investigate a new operator, proposed by combing the already known Hilfer operator and weighted operator with respect to functions, in terms of… read more here.
Keywords: study weighted; respect functions; weighted hilfer; extensive study ... See more keywords
The Duality Theory of Fractional Calculus and a New Fractional Calculus of Variations Involving Left Operators Only
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DOI: 10.1007/s00009-024-02652-x
Abstract: Through duality, it is possible to transform left fractional operators into right fractional operators and vice versa. In contrast to existing literature, we establish integration by parts formulas that exclusively involve either left or right… read more here.
Keywords: theory fractional; calculus variations; fractional calculus; calculus new ... See more keywords
Trends, directions for further research, and some open problems of fractional calculus
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DOI: 10.1007/s11071-021-07158-9
Abstract: The area of fractional calculus (FC) has been fast developing and is presently being applied in all scientific fields. Therefore, it is of key relevance to assess the present state of development and to foresee,… read more here.
Keywords: directions research; fractional calculus; research open; trends directions ... See more keywords
Solutions of the Radial Component of the Fractional Schrödinger Equation Using N-Fractional Calculus Operator
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DOI: 10.1007/s12591-016-0308-8
Abstract: Fractional calculus tecniques are used for the solutions of some classes of differential equations and fractional differential equations. One of the these tecniques is N-fractional calculus operator $$N^{\eta }$$ N η method. We can obtain… read more here.
Keywords: component fractional; fractional calculus; calculus; radial component ... See more keywords
Fractional Calculus Operator Emerging from the 2D Biorthogonal Hermite Konhauser Polynomials
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DOI: 10.1007/s40819-025-01932-8
Abstract: In this paper, we present a novel method for constructing families of two-variable biorthogonal polynomials by utilizing known families of one-variable biorthogonal and orthogonal polynomials. Employing this approach, we define a new class of two-dimensional… read more here.
Keywords: operator; hermite konhauser; fractional calculus; konhauser polynomials ... See more keywords
The solution of certain triple q-integral equations in fractional q-calculus approach
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DOI: 10.1016/j.ajmsc.2018.10.001
Abstract: Abstract In this paper, we consider a certain system of triple q -integral equations, where the kernel is the third Jackson q -Bessel functions. We give two solutions by using the fractional q -calculus approach.… read more here.
Keywords: fractional calculus; solution certain; triple integral; integral equations ... See more keywords
NILT and Prony technique for new definitions of fractional calculus for modeling very slow decay phenomena
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DOI: 10.1016/j.ifacol.2020.12.2053
Abstract: Based on the data from the Tesla users about the degradation of Tesla Model S battery capacity, this paper introduces two new definitions of fractional integrals and derivatives to describe these very slow decay phenomena,… read more here.
Keywords: fractional calculus; decay phenomena; new definitions; definitions fractional ... See more keywords
Estimation of the nitrogen concentration of rubber tree using fractional calculus augmented NIR spectra
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DOI: 10.1016/j.indcrop.2017.06.069
Abstract: Abstract Natural rubber ( Hevea brasiliensis ) is a high-valued industrial crop in tropical areas. Reasonable fertilization can improve the quality and production of the natural rubber. Hence, there is a great interest in developing… read more here.
Keywords: using fractional; fractional calculus; rubber tree; rubber ... See more keywords
Theoretical and mathematical codynamics of nonlinear tuberculosis and COVID-19 model pertaining to fractional calculus and probabilistic approach
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DOI: 10.1038/s41598-024-59261-7
Abstract: Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a novel virus known as coronavirus 2 (SARS-CoV-2) that affects the pulmonary structure and results in the coronavirus illness 2019 (COVID-19). Tuberculosis (TB) and COVID-19 codynamics have… read more here.
Keywords: covid; fractional calculus; infection; tuberculosis covid ... See more keywords
Integrating classical and fractional calculus rheological models in developing hydroxyapatite-enhanced hydrogels
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DOI: 10.1063/5.0213561
Abstract: This study presents a novel method for comprehending the rheological behavior of biomaterials utilized in bone regeneration. The focus is on gelatin, alginate, and hydroxyapatite nanoparticle composites to enhance their mechanical properties and osteoconductive potential.… read more here.
Keywords: integrating classical; calculus rheological; classical fractional; fractional calculus ... See more keywords