A fractional calculus on arbitrary time scales: fractional differentiation and fractional integration
N Benkhettou, AMCB da Cruz, DFM Torres - Signal Processing, 2015 - Elsevier
We introduce a general notion of fractional (noninteger) derivative for functions defined on
arbitrary time scales. The basic tools for the time-scale fractional calculus (fractional …
arbitrary time scales. The basic tools for the time-scale fractional calculus (fractional …
Fractional calculus of variations for a combined Caputo derivative
A Malinowska, D Torres - Fractional Calculus and Applied Analysis, 2011 - degruyter.com
We generalize the fractional Caputo derivative to the fractional derivative CD γα, β, which is
a convex combination of the left Caputo fractional derivative of order α and the right Caputo …
a convex combination of the left Caputo fractional derivative of order α and the right Caputo …
Applications of the novel diamond alpha Hardy–Copson type dynamic inequalities to half linear difference equations
Z Kayar, B Kaymakçalan - Journal of Difference Equations and …, 2022 - Taylor & Francis
This paper is devoted to novel diamond alpha Hardy–Copson type dynamic inequalities,
which are ζ< 0 complements of the classical ones obtained for ζ> 1, and their applications to …
which are ζ< 0 complements of the classical ones obtained for ζ> 1, and their applications to …
[HTML][HTML] Noether's symmetry theorem for nabla problems of the calculus of variations
N Martins, DFM Torres - Applied Mathematics Letters, 2010 - Elsevier
Noether’s symmetry theorem for nabla problems of the calculus of variations - ScienceDirect
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Transversality conditions for infinite horizon variational problems on time scales
Transversality conditions for infinite horizon variational problems on time scales Page 1 Optim
Lett (2011) 5:41–53 DOI 10.1007/s11590-010-0189-7 ORIGINAL PAPER Transversality …
Lett (2011) 5:41–53 DOI 10.1007/s11590-010-0189-7 ORIGINAL PAPER Transversality …
Diamond alpha Bennett‐Leindler type dynamic inequalities and their applications
Z Kayar, B Kaymakçalan… - Mathematical Methods in …, 2022 - Wiley Online Library
In this paper, two kinds of dynamic Bennett‐Leindler type inequalities via the diamond alpha
integrals are derived. The first kind consists of eight new integral inequalities which can be …
integrals are derived. The first kind consists of eight new integral inequalities which can be …
[图书][B] Quantum variational calculus
AB Malinowska, DFM Torres - 2014 - Springer
Many physical phenomena are described by equations involving nondifferentiable functions,
eg, generic trajectories of quantum mechanics (Feynman and Hibbs 1965). Several different …
eg, generic trajectories of quantum mechanics (Feynman and Hibbs 1965). Several different …
Novel diamond alpha Bennett–Leindler type dynamic inequalities and their applications
Z Kayar, B Kaymakçalan - Bulletin of the Malaysian Mathematical …, 2022 - Springer
For the exponent ζ> 1, the diamond alpha Bennett–Leindler type inequalities are
established by developing two methods, one of which is based on the convex linear …
established by developing two methods, one of which is based on the convex linear …
The Riemann-Stieltjes integral on time scales
arXiv:0903.1224v1 [math.CA] 6 Mar 2009 Page 1 THE RIEMANN-STIELTJES INTEGRAL ON
TIME SCALES DOROTA MOZYRSKA, EWA PAWŁUSZEWICZ, AND DELFIM FM TORRES …
TIME SCALES DOROTA MOZYRSKA, EWA PAWŁUSZEWICZ, AND DELFIM FM TORRES …
New Diamond-α Steffensen-Type Inequalities for Convex Functions over General Time Scale Measure Spaces
K Smoljak Kalamir - Axioms, 2022 - mdpi.com
In this paper, we extend some Steffensen-type inequalities to time scales by using the
diamond-α-dynamic integral. Further, we prove some new Steffensen-type inequalities for …
diamond-α-dynamic integral. Further, we prove some new Steffensen-type inequalities for …