Results 21 to 30 of about 13,688 (264)
Проблемы анализа, 2020 Here we present very general iterated fractional Bochner integral representation formulae for Banach space valued functions. Based on these we derive generalized and iterated left and right: fractional Poincar´e type inequalities, fractional Opial type ...
George A. Anastassiou
doaj +1 more source
General Fractional Integrals and Derivatives of Arbitrary Order [PDF]
Symmetry, 2021 In this paper, we introduce the general fractional integrals and derivatives of arbitrary order and study some of their basic properties and particular cases. First, a suitable generalization of the Sonine condition is presented, and some important classes of the kernels that satisfy this condition are introduced.
openaire +2 more sources
Fractal and Fractional, 2022 A general system of fractional differential equations with coupled fractional Stieltjes integrals and a Riemann–Liouville fractional integral in boundary conditions is studied in the context of pattern formation.
Yuan Ma, Dehong Ji
doaj +1 more source
Fractional Integration and Differentiation of the Generalized Mathieu Series [PDF]
Axioms, 2017 We aim to present some formulas for the Saigo hypergeometric fractional integral and differential operators involving the generalized Mathieu series S μ ( r ) , which are expressed in terms of the Hadamard product of the generalized Mathieu series S μ ( r ) and the Fox–Wright function p Ψ q ( z ) .
Ram K. Saxena, Rakesh Kumar Parmar
openaire +4 more sources
ON GENERAL EULERIAN INTEGRAL FORMULAS AND FRACTIONAL INTEGRATION
Tamkang Journal of Mathematics, 1999 In the present work, we evaluate a unified Eulerian type integral whose integrand involves the product of a polynomial system and the multivariable H-function having general arguments. Our integral formula encompasses a very large number of integrals and provides interesting unifieation and extensions of several known (e.g., [1 ...
Gupta, K. C. +2 more
openaire +3 more sources
Generalized Fractional-Order Discrete-Time Integrator [PDF]
Complexity, 2017 We investigate a generalization of discrete-time integrator. Proposed linear discrete-time integrator is characterised by the variable, fractional order of integration/summation. Graphical illustrations of an analysis of particular vector matrices are presented. In numerical examples, we show relations between the order functions and element responses.
Dorota Mozyrska, Piotr Ostalczyk
openaire +3 more sources
Two Integral Representations for the Relaxation Modulus of the Generalized Fractional Zener Model
Fractal and Fractional, 2023 A class of generalized fractional Zener-type viscoelastic models with general fractional derivatives is considered. Two integral representations are derived for the corresponding relaxation modulus. The first representation is established by applying the
Emilia Bazhlekova, Sergey Pshenichnov
doaj +1 more source
Tempered Fractional Integral Inequalities for Convex Functions
Mathematics, 2020 Certain new inequalities for convex functions by utilizing the tempered fractional integral are established in this paper. We also established some new results by employing the connections between the tempered fractional integral with the (R-L ...
Gauhar Rahman +2 more
doaj +1 more source
On generalization conformable fractional integral inequalities
Filomat, 2018 The main issues addressed in this paper are making generalization of Gronwall, Volterra and Pachpatte type inequalities for conformable differential equations. By using the Katugampola definition for conformable calculus we found some upper and lower bound for integral inequalities.
Usta, Fuat, Sarıkaya, Mehmet Zeki
openaire +4 more sources
Fractional Integrals and Generalized Olsen Inequalities
Kyungpook mathematical journal, 2009 Summary: Let \(T_\rho\) be the generalized fractional integral operator associated to a function \(\rho:(0,\infty)\to(0,\infty)\), as defined in [\textit{E. Nakai}, Taiwanese J. Math. 5, No.~3, 587--602 (2001; Zbl 0990.26007)]. For a function \(W\) on \(\mathbb R^n\), we be interested in the boundedness of the multiplication operator \(f\mapsto W\cdot ...
Hendra Gunawan, Eridani
openaire +3 more sources