Results 21 to 30 of about 2,998 (256)
Generalized binomials in fractional calculus
Publicationes Mathematicae Debrecen, 2022 We consider a class of generalized binomials emerging in fractional calculus. After establishing some general properties, we focus on a particular yet relevant case, for which we provide several ready-for-use combinatorial identities, including an adapted version of the Pascal's rule.
D'Ovidio, Mirko +2 more
openaire +2 more sources
General Non-Markovian Quantum Dynamics
Entropy, 2021 A general approach to the construction of non-Markovian quantum theory is proposed. Non-Markovian equations for quantum observables and states are suggested by using general fractional calculus.
Vasily E. Tarasov
doaj +1 more source
Generalized fractional calculus with applications to the calculus of variations
Computers & Mathematics with Applications, 2012 Submitted 22-Dec-2011; revised 26-Jan-2012; accepted 27-Jan-2012; for publication in Computers and Mathematics with ...
Tatiana Odzijewicz +2 more
openaire +5 more sources
Coordination of Classical and Dynamic Inequalities Complying on Time Scales
European Journal of Mathematical Analysis, 2023 In this research article, we present extensions of some classical inequalities such as Schweitzer, Pólya–Szegö, Kantorovich and Greub–Rheinboldt inequalities of fractional calculus on time scales. To investigate generalizations of such types of classical
Muhammad Jibril Shahab Sahir
doaj +1 more source
Zener Model with General Fractional Calculus: Thermodynamical Restrictions
Fractal and Fractional, 2022 We studied a Zener-type model of a viscoelastic body within the context of general fractional calculus and derived restrictions on coefficients that follow from the dissipation inequality, which is the entropy inequality under isothermal conditions.
Teodor M. Atanackovic, Stevan Pilipovic
doaj +1 more source
Fractional calculus of variations with a generalized fractional derivative [PDF]
Fractional Differential Calculus, 2016 Summary: In this paper, we introduce a generalization of the Hilfer-Prabhakar derivative and obtain the Euler-Lagrange equations and Hamiltonian formulation with respect to this fractional derivative in the theory of fractional calculus of variations. Also, we get a sufficient condition for optimality.
Askari, Hassan, Ansari, Alireza
openaire +2 more sources
Operational Calculus for the General Fractional Derivatives of Arbitrary Order
Mathematics, 2022 In this paper, we deal with the general fractional integrals and the general fractional derivatives of arbitrary order with the kernels from a class of functions that have an integrable singularity of power function type at the origin.
Maryam Al-Kandari +2 more
doaj +1 more source
Mathematics, 2023 Significant progress has been made in incorporating fractional calculus into the projection and lag synchronization of complex networks. However, real-world networks are highly complex, making the fractional derivative used in complex dynamics more ...
Zhenduo Sun +2 more
doaj +1 more source
On the 1st-Level General Fractional Derivatives of Arbitrary Order
Fractal and Fractional, 2023 In this paper, the 1st-level general fractional derivatives of arbitrary order are defined and investigated for the first time. We start with a generalization of the Sonin condition for the kernels of the general fractional integrals and derivatives and ...
Yuri Luchko
doaj +1 more source
General Fractional Integrals and Derivatives with the Sonine Kernels
Mathematics, 2021 In this paper, we address the general fractional integrals and derivatives with the Sonine kernels on the spaces of functions with an integrable singularity at the point zero.
Yuri Luchko
doaj +1 more source