Existence of Positive Solutions for m-Point Boundary Value Problem for Nonlinear Fractional Differential Equation

We investigate an m-point boundary value problem for nonlinear fractional differential equations. The associated Green function for the boundary value problem is given at first, and some useful properties of the Green function are obtained. By using the fixed point theorems of cone expansion and compression of norm type and Leggett-Williams fixed point theorem, the existence of multiple positive solutions is obtained

Derivative-order-dependent stability and transient behaviour in a predator–prey system of fractional differential equations

In this paper, the static and dynamic behaviour of a fractional-order predator–prey model are studied, where the nonlinear interactions between the two species lead to multiple stable states. As has been found in many previous systems, the stability of such states can be dependent on the fractional order of the time derivative, which is included as a phenomenological model of memory-effects in the predator and prey species. However, what is less well understood is the transient behaviour and dependence of the observed domains of attraction for each stable state on the order of the fractional time derivative. These dependencies are investigated using analytical (for the stability of equilibria) and numerical (for the observed domains of attraction) techniques. Results reveal far richer dynamics compared to the integer-order model. We conclude that, as well as the species and controllable parameters, the memory effect of the species will play a role in the observed behaviour of the system

Morphological and molecular characterization of somaclonal variations in tissue culture-derived banana plants

AbstractIn this study, 40000 tissue culture-derived banana plants (vitroplants) at different growth stages, i.e. acclimatization, nursery and open field of banana (Musa spp.) cultivar ‘Grand Naine’ were screened for somaclonal variations using morphological investigations and molecular characterization. The total detected variants were grouped into 25 off-types (two of them died) in addition to the normal plant. Random Amplified Polymorphic DNA (RAPD) was carried out to study the differences among the normal cultivar ‘Grand Naine’ and its 23 variants using 17 arbitrary primers. Cluster analysis results revealed that ‘winged petiole’ and ‘deformed lamina’ were more related to the normal plant. However, ‘Giant plant’ and ‘weak plant’ related to each other and clustered with normal plant. According to principal coordinate analysis, most of the variants were aggregated nearly, whereas ‘variegated plant’ was separated apart from the other variants. This may reflect the genetic difference between ‘variegated plant’ and the other variants. The results obtained from both molecular and morphological analyses were in contiguous with better resolution when using the PCOORDA analysis than cluster analysis. Thus, it can be said that molecular markers can be used to eliminate the undesirable somaclonal variants from the lab without additional culture of the vitroplants in the field in order to save time and efforts

Fractional calculus model of GATA-switching for regulating the differentiation of a hematopoietic stem cell

This paper deals with the fractional order model for GATA-switching for regulating the differentiation of a hematopoietic stem cell. We give a detailed analysis for the asymptotic stability of the model. The Adams-Bashforth-Moulton algorithm has been used to solve and simulate the system of differential equations

Enhancement of clavulanic acid production by Streptomyces sp MU-NRC77 via mutation and medium optimization

Purpose: To enhance clavulanic acid production using UV-mutagenesis on Streptomyces sp. NRC77.Methods: UV-mutagenesis was used to study the effect of Streptomyces sp. NRC77 on CA production. Phenotypic and genotypic identification methods of the promising mutant strain were characterized. Optimization of the fermentation medium and culture conditions were investigatedResults: Out of the screened mutants, 120A3 mutant isolate was selected as promising. The phenotypic properties of 120A3 mutant showed culture characteristics similar to those of Streptomyces species. Phylogenetic analysis of 16S rRNA gene sequence indicate that this strain has similarity (99 %) to Streptomyces sp.T2-7; therefore it was suggested as Streptomyces sp. MU-NRC77 and has Gen Bank accession no. KT953342.Conclusion: Improvement of CA yield by 48 % was obtained from fermentation medium and culture condition optimization. Further optimization by addition of H2O2 and activated charcoal to the production medium increased CA yield to 646.12 and 682.94 mg/L respectively, i.e., 83 % more than that obtained prior to addition.Keywords: Clavulanic acid, Medium optimization, Phenotypic and Genotypic identification, Streptomyces sp. MU-NRC77, UV-Mutagenesi

Monotone iterative procedure and systems of a finite number of nonlinear fractional differential equations

The aim of the paper is to present a nontrivial and natural extension of the comparison result and the monotone iterative procedure based on upper and lower solutions, which were recently established in (Wang et al. in Appl. Math. Lett. 25:1019-1024, 2012), to the case of any finite number of nonlinear fractional differential equations.The author is very grateful to the reviewers for the remarks, which improved the final version of the manuscript. This article was financially supported by University of Łódź as a part of donation for the research activities aimed at the development of young scientists, grant no. 545/1117