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In this article, we extend the generalized invexity and duality results for multiobjective variational problems with fractional derivative pertaining to an exponential kernel by using the concept of weak minima. Multiobjective variational problems find their applications in economic planning, flight control design, industrial process control, control of space structures, control of production and inventory, advertising investment, impulsive control problems, mechanics, and several other engineering and scientific problems. The proposed work considers the newly derived Caputo–Fabrizio (CF) fractional derivative operator. It is actually a convolution of the exponential function and the first-order derivative. The significant characteristic of this fractional derivative operator is that it provides a non-singular exponential kernel, which describes the dynamics of a system in a better way. Moreover, the proposed work also presents various weak, strong, and converse duality theorems under the diverse generalized invexity conditions in view of the CF fractional derivative operator.

In this paper, we investigate the fractal nature of the local fractional Landau–Ginzburg–Higgs Equation (LFLGHE) describing nonlinear waves with weak scattering in a fractal medium. The main goal of the paper is to introduce and apply the Local Fractional Elzaki Variational Iteration Method (LFEVIM) for solution of LFLGHE. Convergence analysis of LFEVIM solution for general nonlinear local fractional partial differential equation is also provided. Two examples of the local fractional LFLGHE are considered to demonstrate the applicability of the proposed technique with numerical simulations on Cantor set. [ABSTRACT FROM AUTHOR]

In this paper, a fractional food chain system consisting of a Holling type II functional response was studied in view of a fractional derivative operator. The considered fractional derivative operator provided nonsingular as well as a nonlocal kernel which was significantly better than other derivative operators. Fractional order modeling of a model was also useful to model the behavior of real systems and in the investigation of dynamical systems. This model depicted the relationship among four types of species: prey, susceptible intermediate predators (IP), infected intermediate predators, and apex predators. One of the significant aspects of this model was the inclusion of Michaelis-Menten type or Holling type II functional response to represent the predator-prey link. A functional response depicted the rate at which the normal predator consumed the prey. The qualitative property and assumptions of the model were discussed in detail. The present work discussed the dynamics and analytical behavior of the food chain model in the context of fractional modeling. This study also examined the existence and uniqueness related analysis of solutions to the food chain system. In addition, the Ulam-Hyers stability approach was also discussed for the model. Moreover, the present work examined the numerical approach for the solution and simulation for the model with the help of graphical presentations. [ABSTRACT FROM AUTHOR]

This study performs the time series analysis of agriculture land in the Nainital District of Uttarakhand, India. The study utilizes Landsat satellite images for the classification of agriculture and non-agriculture land over a time duration of 21 years (2000–2021). Landsat 5, 7 and 8 satellites data have been used to classify the study area with Random Forest classifier. The Landsat satellite images are processed using the Google Earth Engine (GEE) platform. The selection of Random Forest classier has been based on a comparative analysis among Random Forest (RF), Support Vector Machines (SVM) and Classification and Regression Trees (CART). Overall accuracy, user accuracy and producer accuracy and Kappa coefficient has been evaluated to determine the best classifier for the study area. The overall accuracy for RF, SVM and CART for the year 2021 is 96.38%, 94.44% and 91.94% respectively. Similarly, the Kappa coefficient for RF, SVM and CART was 0.96, 0.89, 0.81 respectively. The classified images of Landsat in agriculture and non-agriculture area over a period of 21 years (2000–2021) shows a decrement of 4.71% in agriculture land which is quite significant. This study has also shown that the maximum decrease in agriculture area in last four years, i.e., from 2018 to 2021. This kind of study is very important for a developing country to access the change and take proper measure so that flora and fauna of the region can be maintained. [ABSTRACT FROM AUTHOR]

In this paper, the Kharrat–Toma transforms of the Prabhakar integral, a Hilfer–Prabhakar (HP) fractional derivative, and the regularized version of the HP fractional derivative are derived. Moreover, we also compute the solution of some Cauchy problems and diffusion equations modeled with the HP fractional derivative via Kharrat–Toma transform. The solutions of Cauchy problems and the diffusion equations modeled with the HP fractional derivative are computed in the form of the generalized Mittag–Leffler function. [ABSTRACT FROM AUTHOR]

In this paper, we implement computational methods, namely the local fractional natural homotopy analysis method (LFNHAM) and local fractional natural decomposition method (LFNDM), to examine the solution for the local fractional Lighthill–Whitham–Richards (LFLWR) model occurring in a fractal vehicular traffic flow. The LWR approach preferably models the traffic flow and represents the traffic patterns via the supposition of speed–density equilibrium relationship and continuity equation. This model is mostly preferred for modeling of traffic flow because of its simple approach and interpretive ability to examine the qualitative patterns of traffic flow. The methods applied here incorporate the local fractional natural transform (LFNT) and derive the solutions for the LFLWR model in a closed form. Two examples are provided to demonstrate the accuracy and efficiency of the suggested methods. Furthermore, the numerical simulations have also been presented for each of the examples in the fractal domain. Additionally, the explored solutions for both examples have also been compared and are in good match with already existing solutions in literature. The methods applied in this work make the computational process easier as compared to other iterative methods and still provide precise solutions. [ABSTRACT FROM AUTHOR]

In this paper, we implement the semi‐analytical schemes, namely, local fractional homotopy perturbation Sumudu transform method (LFHPSTM) and local fractional homotopy analysis Sumudu transform method (LFHASTM), for finding the approximate analytical solutions of local fractional Laplace equations under different initial conditions on Cantor sets. The novelty of the work lies in the application of these suggested schemes which were never used to solve the local fractional Laplace equation. The Laplace equation mainly contributes to electrostatistics, mechanical engineering, and theoretical physics. This equation also helps in formulation of the electrostatic problem of a rod under a torsion load. Moreover, it helps in handling potential field problems also. These aspects enhance the significance of getting a solution of the local fractional Laplace equation in fractal media. The suggested methods are copulation of local fractional homotopy perturbation method and local fractional homotopy analysis method with the local fractional Sumudu transform, respectively. The computational process indicates that the schemes are very efficient to obtain nondifferentiable solutions for given equations in a smooth way. Moreover, the solution analysis depicts that both the local fractional hybrid homotopy schemes are in a good agreement with each other. These methods depict the accuracy and efficiency of the implemented methods in view of correspondence with solutions obtained with other methods in previous works. The numerical simulations for obtained results are discussed for various values of order of a local fractional derivative. The 3D graphs on the Cantor set are constructed with the help of Matlab software. [ABSTRACT FROM AUTHOR]

This research paper implements the fractional homotopy analysis transform technique to compute the approximate analytical solution of the nonlinear three-species food chain model with time-fractional derivatives. The offered technique is a fantastic blend of homotopy analysis method (HAM) and Laplace transform (LT) operator and has been used fruitfully in the numerical computation of various fractional differential equations (FDEs). This paper involves the fractional derivatives of Caputo style. The numerical solutions of this selected fractional-order food chain model are evaluated by making use of the associated initial conditions. It is revealed by the adopting procedure that the more desirable estimation of the solution can be easily acquired through the calculation of some number of iteration terms only — a fact which authenticates the easiness and soundness of the suggested hybrid scheme. The variations of fractional order of time derivative on the solutions for different specific cases have been depicted through graphical presentations. The outcomes demonstrated through the graphs expound that the adopted scheme is very fantastic and accurate. [ABSTRACT FROM AUTHOR]

Approximate analytical solution of the system of coupled nonlinear Ordinary Differential Equations (ODEs) of a biochemical reaction model is much relevant due to its practical significance to biochemists. In this paper, an effective and powerful mathematical technique, viz. fractional homotopy analysis transform method (FHATM), is employed to get the numerical solutions of biochemical reaction model with time fractional derivatives. The adopted scheme is the beautiful copulation of homotopy analysis technique and Laplace transform algorithm. This paper shows that the adopted scheme is quite easy as well as computationally attractive in the context of a solution procedure. The Caputo-type fractional derivatives are considered in the present paper. Approximate results of the probability density functions of the time fractional biochemical reaction model are computed for miscellaneous fractional Brownian motions as well as for classical motion and are presented graphically. The time fractional biochemical reaction model with respect to stability analysis for various values of fractional order q is also analyzed. In the context of stability discussion, we have used the fractional Routh–Hurwitz stability criterion to establish the local stability of the biochemical reaction model of fractional order. [ABSTRACT FROM AUTHOR]

In this work, we investigate solutions for the local fractional Helmholtz and Laplace equations on Cantor set having importance in electrostatics, gravitation and uid dynamics. To find exact solutions, the q-local fractional homotopy analysis transform method (q-LFHATM) has been used. The numerical results computed with the aid of the applied scheme shows that it is an efficient and accurate tool to solve differential equations with local fractional derivatives. [ABSTRACT FROM AUTHOR]

Abstract: Salivary glands, although widely considered as typically exocrine, may also release specific proteins in an endocrine manner. However, endocrine release of salivary gland proteins is not generally acknowledged since the evidences are not easily demonstrable. Submandibular salivary glands (SMG) of male Syrian hamsters express male-specific secretory proteins (MSP; which are lipocalins) visible in SDS–PAGE of SMG extracts, as major bands and also detectable in immunoblots of whole-saliva and urine as low MSP crossreactions. We report here that MSP is localized in acinar cells of SMG and acute treatment with isoproterenol (IPR; non-specific β1/β2-adrenergic agonist) results in considerable release of MSP in SMG-saliva. Moreover, acute IPR treatment markedly depletes SMG-MSP in a dose- and time-dependent manner. However, MSP depleted from SMG, far exceeds that recovered in SMG-saliva. Blood, submandibular lymph nodes and kidney of IPR-treated males showed MSP crossreactions and SDS–PAGE of their urine revealed profuse MSP excretion; this was undetectable in IPR-treated-SMG-ablated males, confirming that a substantial amount of MSP depleted from SMG after IPR treatment enters circulation and is excreted in urine. Treatments with specific β1- or β2-adrenergic agonists also reduced SMG-MSP levels and resulted in copious urinary excretion of MSP. Co-treatments with specific β1/β2-blockers indicated that above effects of IPR, β1- and even β2-agonists are very likely mediated by β1-adrenoceptors. MSP’s detection by SDS–PAGE in urine after β-agonist treatment is a compelling and easily demonstrable evidence of release into circulation of a salivary gland protein. The possible means (endocrine-like or otherwise) of MSP’s release into circulation and significance of its presence in saliva, blood and urine of male hamsters are discussed. [Copyright &y& Elsevier]

Proteins belonging to the lipocalin superfamily are usually secretory proteins of molecular mass ∼20 kDa with a hydrophobic pocket for the binding and transport of diverse small ligands. Various lipocalins have been associated with many biological processes, e.g. immunomodulation, odorant transport, pheromonal activity, retinoid transport, cancer-cell interactions etc. However, the exact functions of many lipocalins and the ligands bound by them are unclear. Previously, the cDNA of a 20 kDa lipocalin (FLP) which is female-specifically expressed in the lacrimal glands of Syrian (golden) hamsters and secreted in the tears of females has been identified and cloned. His-tagged recombinant FLP (rFLP) has now been cloned, overexpressed in Escherichia coli as a soluble protein and purified to homogeneity using Ni-affinity followed by size-exclusion chromatography. Purified rFLP was crystallized using the sitting-drop vapour-diffusion method. The crystals tested belonged to space group P212121 and diffracted to beyond 1.86 Å resolution. Solvent-content analysis indicated the presence of one monomer in the asymmetric unit. [ABSTRACT FROM AUTHOR]