Caputo Derivatives in Viscoelasticity: A Non-Linear Finite-Deformation Theory for Tissue

Mathematics Subject Classification: 26A33, 74B20, 74D10, 74L15

Eigenfunctions and fundamental solutions of the Caputo fractional Laplace and Dirac operators

In this paper, by using the method of separation of variables, we obtain eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator defined via fractional Caputo derivatives. The solutions are expressed using the Mittag-Leffler function and we show some graphical representations for some parameters. A family of fundamental solutions of the corresponding fractional Dirac operator is also obtained. Particular cases are considered in both cases.

An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance index

The shifted Legendre orthogonal polynomials are used for the numerical solution of a new formulation for the multi-dimensional fractional optimal control problem (M-DFOCP) with a quadratic performance index. The fractional derivatives are described in the Caputo sense. The Lagrange multiplier method for the constrained extremum and the operational matrix of fractional integrals are used together with the help of the properties of the shifted Legendre orthonormal polynomials. The method reduces the M-DFOCP to a simpler problem that consists of solving a system of algebraic equations. For confirming the efficiency and accuracy of the proposed scheme, some test problems are implemented with their approximate solutions.

Fractional variational problems depending on indefinite integrals and with delay

The aim of this paper is to exhibit a necessary and sufficient condition of optimality for functionals depending on fractional integrals and derivatives, on indefinite integrals and on presence of time delay. We exemplify with one example, where we nd analytically the minimizer.

On the Equivalence of the Riemann-Liouville and the Caputo Fractional Order Derivatives in Modeling of Linear Viscoelastic Materials

Mathematics Subject Classification: 26A33

Efficient Legendre spectral tau algorithm for solving two-sided space-time Caputo fractional advection-dispersion equation

In this paper we present the operational matrices of the left Caputo fractional derivative, right Caputo fractional derivative and Riemann–Liouville fractional integral for shifted Legendre polynomials. We develop an accurate numerical algorithm to solve the two-sided space–time fractional advection–dispersion equation (FADE) based on a spectral shifted Legendre tau (SLT) method in combination with the derived shifted Legendre operational matrices. The fractional derivatives are described in the Caputo sense. We propose a spectral SLT method, both in temporal and spatial discretizations for the two-sided space–time FADE. This technique reduces the two-sided space–time FADE to a system of algebraic equations that simplifies the problem. Numerical results carried out to confirm the spectral accuracy and efficiency of the proposed algorithm. By selecting relatively few Legendre polynomial degrees, we are able to get very accurate approximations, demonstrating the utility of the new approach over other numerical methods.

Caputo-Type Modification of the Erdélyi-Kober Fractional Derivative

2000 Math. Subject Classification: 26A33; 33E12, 33E30, 44A15, 45J05

Time-Fractional Derivatives in Relaxation Processes: A Tutorial Survey

2000 Mathematics Subject Classification: 26A33, 33E12, 33C60, 44A10, 45K05, 74D05,

Fractional Derivatives in Spaces of Generalized Functions

MSC 2010: 26A33, 46Fxx, 58C05 Dedicated to 80-th birthday of Prof. Rudolf Gorenflo

Fractional differential equations with dependence on the Caputo-Katugampola derivative

In this paper we present a new type of fractional operator, the Caputo–Katugampola derivative. The Caputo and the Caputo–Hadamard fractional derivatives are special cases of this new operator. An existence and uniqueness theorem for a fractional Cauchy type problem, with dependence on the Caputo–Katugampola derivative, is proven. A decomposition formula for the Caputo–Katugampola derivative is obtained. This formula allows us to provide a simple numerical procedure to solve the fractional differential equation.

Design, Synthesis And Biological Evaluation Of Hybrid Bioisoster Derivatives Of N-acylhydrazone And Furoxan Groups With Potential And Selective Anti-trypanosoma Cruzi Activity.

Hybrid bioisoster derivatives from N-acylhydrazones and furoxan groups were designed with the objective of obtaining at least a dual mechanism of action: cruzain inhibition and nitric oxide (NO) releasing activity. Fifteen designed compounds were synthesized varying the substitution in N-acylhydrazone and in furoxan group as well. They had its anti-Trypanosoma cruzi activity in amastigotes forms, NO releasing potential and inhibitory cruzain activity evaluated. The two most active compounds (6, 14) both in the parasite amastigotes and in the enzyme contain the nitro group in para position of the aromatic ring. The permeability screening in Caco-2 cell and cytotoxicity assay in human cells were performed for those most active compounds and both showed to be less cytotoxic than the reference drug, benznidazole. Compound 6 was the most promising, since besides activity it showed good permeability and selectivity index, higher than the reference drug. Thereby the compound 6 was considered as a possible candidate for additional studies.

Synthesis And Antiproliferative Activity Of 8-hydroxyquinoline Derivatives Containing A 1,2,3-triazole Moiety.

Twelve novel 8-hydroxyquinoline derivatives were synthesized with good yields by performing copper-catalyzed Huisgen 1,3-dipolar cycloaddition (click reaction) between an 8-O-alkylated-quinoline containing a terminal alkyne and various aromatic or protected sugar azides. These compounds were evaluated in vitro for their antiproliferative activity on various cancer cell types. Protected sugar derivative 16 was the most active compound in the series, exhibiting potent antiproliferative activity and high selectivity toward ovarian cancer cells (OVCAR-03, GI50 < 0.25 μg mL(-1)); this derivative was more active than the reference drug doxorubicin (OVCAR-03, GI50 = 0.43 μg mL(-1)). In structure-activity relationship (SAR) studies, the physico-chemical parameters of the compounds were evaluated and docking calculations were performed for the α-glucosidase active site to predict the possible mechanism of action of this series of compounds.

Design And Synthesis Of N-acylated Aza-goniothalamin Derivatives And Evaluation Of Their In Vitro And In Vivo Antitumor Activity.

Herein we describe the synthesis of a focused library of compounds based on the structure of goniothalamin (1) and the evaluation of the potential antitumor activity of the compounds. N-Acylation of aza-goniothalamin (2) restored the in vitro antiproliferative activity of this family of compounds. 1-(E)-But-2-enoyl-6-styryl-5,6-dihydropyridin-2(1H)-one (18) displayed enhanced antiproliferative activity. Both goniothalamin (1) and derivative 18 led to reactive oxygen species generation in PC-3 cells, which was probably a signal for caspase-dependent apoptosis. Treatment with derivative 18 promoted Annexin V/7-aminoactinomycin D double staining, which indicated apoptosis, and also led to G2 /M cell-cycle arrest. In vivo studies in Ehrlich ascitic and solid tumor models confirmed the antitumor activity of goniothalamin (1), without signs of toxicity. However, derivative 18 exhibited an unexpectedly lower in vivo antitumor activity, despite the treatments being administered at the same site of inoculation. Contrary to its in vitro profile, aza-goniothalamin (2) inhibited Ehrlich tumor growth, both on the ascitic and solid forms. Our findings highlight the importance of in vivo studies in the search for new candidates for cancer treatment.

Esi(+)-ms And Gc-ms Study Of The Hydrolysis Of N-azobenzyl Derivatives Of Chitosan.

New N-p-chloro-, N-p-bromo-, and N-p-nitrophenylazobenzylchitosan derivatives, as well as the corresponding azophenyl and azophenyl-p-sulfonic acids, were synthesized by coupling N-benzylvchitosan with aryl diazonium salts. The synthesized molecules were analyzed by UV-Vis, FT-IR, 1H-NMR and 15N-NMR spectroscopy. The capacity of copper chelation by these materials was studied by AAS. Chitosan and the derivatives were subjected to hydrolysis and the products were analyzed by ESI(+)-MS and GC-MS, confirming the formation of N-benzyl chitosan. Furthermore, the MS results indicate that a nucleophilic aromatic substitution (SnAr) reaction occurs under hydrolysis conditions, yielding chloroaniline from N-p-bromo-, and N-p-nitrophenylazo-benzylchitosan as well as bromoaniline from N-p-chloro-, and N-p-nitrophenylazobenzyl-chitosan.

Antioxidant and antimicrobial properties of 2-(4,5-dihydro-1H-pyrazol-1-yl)-pyrimidine and 1-carboxamidino-1H-pyrazole derivatives

Five previously synthesized 4-trifluoromethyl-2-(5-aryl-3-styryl-1H-pyrazol-1yl)-pyrimidines and six 5-aryl-3-styryl-1-carboxamidino-1H-pyrazole derivatives were screened for their antioxidant proprieties. The antioxidant activities were evaluated by using the DPPH and the HRP/luminol/H2O2 chemiluminescence assay systems and for their antimicrobial activity (MIC). The results were good for those series in some concentration in comparison with the standards.