Results 71 to 80 of about 8,512 (209)

A New Gronwall–Bellman Inequality in Frame of Generalized Proportional Fractional Derivative

Mathematics, 2019
New versions of a Gronwall−Bellman inequality in the frame of the generalized (Riemann−Liouville and Caputo) proportional fractional derivative are provided.
Jehad Alzabut, Weerawat Sudsutad, Zeynep Kayar, Hamid Baghani   +3 more
doaj   +1 more source

Fractional variational calculus of variable order

, 2012
We study the fundamental problem of the calculus of variations with variable order fractional operators. Fractional integrals are considered in the sense of Riemann-Liouville while derivatives are of Caputo type.Comment: Submitted 26-Sept-2011; accepted ...
A Almeida, AA Kilbas, AB Malinowska, B Brunt van, B Ross, CF Lorenzo, CFM Coimbra, D Mozyrska, D Mozyrska, F. Riewe, F. Riewe, G Diaz, GSF Frederico, GSF Frederico, HTC Pedro, J. Cresson, JA Tenreiro Machado, LES Ramirez, M Klimek, M Klimek, M Klimek, M Klimek, M Klimek, NRO Bastos, NRO Bastos, P Ivady, R Almeida, R. Almeida, SG Samko, SG Samko, SG Samko, T Odzijewicz, T Odzijewicz, TM Atanackovic   +33 more
core   +1 more source

Integral-Type Fractional Equations with a Proportional Riemann–Liouville Derivative [PDF]

Journal of Mathematics, 2021
In this paper, we present the necessary conditions where integral-type fractional equations with a proportional Riemann–Liouville derivative have a unique solution. Also, we give an example to illustrate our work.
openaire   +2 more sources

Finite Biorthogonal Polynomials Suggested by the Finite Orthogonal Polynomials Mnp,qx$$ {M}_n^{\left(p,q\right)}(x) $$

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT Constructing a biorthogonal structure from scratch, that is, defining a biorthogonal pair is quite tough. Because here the orthogonality must be established between two different sets. There are four known univariate biorthogonal polynomial sets, suggested by Laguerre, Jacobi, Hermite and Szegő‐Hermite polynomials, in the literature.
Esra Güldoğan Lekesiz
wiley   +1 more source

Fractional Calculus of Variations for Double Integrals [PDF]

, 2011
We consider fractional isoperimetric problems of calculus of variations with double integrals via the recent modified Riemann-Liouville approach. A necessary optimality condition of Euler-Lagrange type, in the form of a multitime fractional PDE, is ...
Odzijewicz, Tatiana, Torres, Delfim F. M.   +1 more
core   +3 more sources

Fractional Vector Calculus and Fractional Maxwell's Equations

, 2011
The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. The main approaches to formulate a FVC, which are used in the
Belleguie, Ben Adda, Ben Adda, Ben Adda, Ben Adda, Brandt, Chen, Cottrill-Shepherd, Engheta, Foley, Gelfand, Genchev, Hussain, Hussain, Kazbekov, Kilbas, Kiryakova, Laskin, Mashhoon, Mashhoon, Mashhoon, McBride, Meerschaert, Metzler, Metzler, Miller, Montroll, Naqvi, Naqvi, Nishimoto, Oldham, Pierantozzi, Podlubny, Ross, Rubin, Samko, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Vasily E. Tarasov, West, Zaslavsky, Zaslavsky   +55 more
core   +1 more source

Capturing Complex Rate‐Dependent Behaviors of Saturated Clays: A Fractional Consistency Kinematic Hardening Viscoplastic Approach

International Journal for Numerical and Analytical Methods in Geomechanics, EarlyView.
ABSTRACT Saturated high plasticity clays show complex nonlinear, rate‐dependent, and hysteresis behaviors under non‐monotonic stress paths, requiring advanced mathematical constitutive equations for accurate description. Taking into account the inherent advantages of kinematic hardening mechanisms in simulating complex stress histories, this paper ...
Wei Cheng, Zhen‐Yu Yin
wiley   +1 more source

On an Inequality of H. G. Hardy

Journal of Inequalities and Applications, 2010
We state, prove, and discuss new general inequality for convex and increasing functions. As a special case of that general result, we obtain new fractional inequalities involving fractional integrals and derivatives of Riemann-Liouville type ...
Krulić Kristina, Iqbal Sajid, Pečarić Josip   +2 more
doaj  

Euler-Maclaurin-type Inequalities for $h-$convex Functions via Riemann-Liouville Fractional Integrals

Communications in Advanced Mathematical Sciences
In this paper, some Euler-Maclaurin-type inequalities are established by using $h-$convex functions involving Riemann-Liouville fractional integrals.
Hüseyin Budak, Fatih Hezenci
doaj   +1 more source

Positive solutions for a system of Riemann–Liouville fractional boundary value problems with p-Laplacian operators

Advances in Difference Equations, 2020
We study the existence and nonexistence of positive solutions for a system of Riemann–Liouville fractional differential equations with p-Laplacian operators, nonnegative nonlinearities and positive parameters, subject to coupled nonlocal boundary ...
Alexandru Tudorache, Rodica Luca
doaj   +1 more source