Existence Theory of Differential Equations of Arbitrary Order

The aims of this chapter are devoted to investigate a system of fractional-order differential equations (FDEs) with multipoint boundary conditions. Necessary and sufficient conditions are investigated for at most one solution to the proposed problem. Also, results for the existence of at least one or two positive solutions are developed by using a fixed-point theorem of concave-type operator for the considered problem. Further, we extend the conditions for more than two solutions and established some adequate conditions for multiplicity results to the proposed problem. Also, a result devoted to Hyers-Ulam stability is discussed. Suitable examples are provided to verify the established results

Immediate hypersensitivity reaction with mango

Hypersensitivity to the fruit mango is extremely rare and can exhibit either as immediate or delayed reactions. Since 1939, only 22 patients (10 with immediate type I reactions and 12 with delayed) have been documented with allergy to mango. History of atopy and geographical region may influence the type of reaction. Immediate reactions occured most often in patients with history of atopy, while delayed reactions developed in non-atopic individuals. Clustering of delayed hypersensitivity reports from Australia and immediate reactions from Europe has been documented. We report a 50-year-old man with immediate type I hypersensitivity to mango, who developed cough, wheezing dyspnoea, generalised itching and abdominal discomfort after ingestion of mango. Life threatening event can also happen making it imperative to diagnose on time, so as to prevent significant morbidity and potential mortalityNadwrażliwość na owoce mango jest bardzo rzadkim zjawiskiem i może przebiegać zarówno jako reakcja natychmiastowa, jak i opóźniona. Od 1939 roku udokumentowano alergię na mango tylko u 22 pacjentów (u 10 z reakcjami typu natychmiastowego i u 12 z reakcją opóźnioną). Wydaje się, że wywiad atopowy oraz region geograficzny mogą wpływać na rodzaj reakcji. Natychmiastowe reakcje obserwowano najczęściej u pacjentów z wywiadem atopii, natomiast reakcje opóźnione byłych częstsze u pacjentów bez takiego wywiadu. Dane epidemiologiczne wskazują, że na terenie Australii dominuje nadwrażliwość z opóźnionym typem reakcji, w Europie zaś przeważają reakcje typu natychmiastowego. W pracy przedstawiono przypadek 50-letniego mężczyzny z nadwrażliwością typu I natychmiastowego na alergeny owocu mango, u którego po spożyciu mango wystąpił kaszel, świszczący oddech i duszność, uogólniony świąd skóry i dolegliwości brzuszne. Diagnostyka w takich sytuacjach powinna być przeprowadzona możliwie szybko, aby wdrożyć wtórną profilaktykę, uniknąć ekspozycji i zapobiegać stanom zagrażającym życiu w przebiegu nadwrażliwości

Numerical Solutions of Coupled Systems of Fractional Order Partial Differential Equations

We develop a numerical method by using operational matrices of fractional order integrations and differentiations to obtain approximate solutions to a class of coupled systems of fractional order partial differential equations (FPDEs). We use shifted Legendre polynomials in two variables. With the help of the aforesaid matrices, we convert the system under consideration to a system of easily solvable algebraic equation of Sylvester type. During this process, we need no discretization of the data. We also provide error analysis and some test problems to demonstrate the established technique

On a Hybrid Technique to Handle Analytical and Approximate Solutions of Linear and Nonlinear Fractional Order Partial Differential Equations

This manuscript is devoted to consider Natural transform (NT) coupled with homotopy perturbation method (HPM) for obtaining series solutions to some linear and nonlinear fractional partial differential equations (FPDEs). By means of NT, we obtain the transformed problem which is then solved by using HPM. By means of Stehfest’s numerical algorithm and using the dual relationship of NT and Laplace transform, we calculate inverse NT for approximate solutions. The series solutions we obtain using the proposed method are in close agreement with the exact solutions. We apply the proposed method to some interesting problems to illustrate our main results

Middle lobe syndrome: an extraordinary presentation of endobronchial tuberculosis

Tuberculous infection of the tracheobronchial tree, termed as endobronchial tuberculosis (EBTB), is more common in young adults and females. This clinical entity is poorly understood and the diagnosis is frequently delayed as sputum smears are often negative for acid fast bacilli and the chest radiograph can be normal, resulting in diagnostic confusion. Bronchoscopy continues to play a key role in its diagnosis. Though atelectasis is not uncommon in these patients, EBTB presenting as a middle lobe syndrome (MLS) has rarely been documented. MLS refers to chronic or recurrent collapse of the right middle lobe and has a myriad of causes. The pathogenesis of this entity too is not fully established. We report this exceptional clinical manifestation in a 19-year-old male, who presented for evaluation of respiratory symptoms for 6 months along with constitutional complaints. Imaging suggested the presence of MLS and bronchoscopy established the diagnosis of endobronchial tuberculosis. GeneXpert evaluation of bronchial aspirate detected Mycobacterium tuberculosis. Histopathology confirmed the presence of granulomatous lesions. Subsequently, the cultures of bronchial aspirate and post-bronchoscopy sputum grew M. tuberculosis. Appropriate therapy with anti-tuberculosis drugs resulted in a remarkable symptomatic and radiological improvement. EBTB presenting as a MLS is a distinct rarity

Customers’ Intention towards Purchasing Apartment in Dhaka City, Bangladesh: Offering an Alternative Buying Intention Model

Various models and theories have been proposed to explain customers’ buying attitude, buying intention and behavior. Taking a new approach this study has applied the theory of planned behavior to explain buying intention in context of Real Estate especially on apartment buying behavior. This study has aimed at exploring the antecedents of customers’ buying attitude and investigating the impact of customers’ buying attitude on buying intention. A questionnaire survey method has been used with 275 customers and response rate of 86.18 percent. Initially an Exploratory Factor Analysis has been directed using SPSS (Version 21).We have explored six factors project facilities, environmental issues, location and communication, physical quality, promotion and prices that act as antecedents of customers’ buying attitude. After that, CFA has been carried out to confirm the factors. Structural Equation Modeling (SEM) has been used to test both the proposed model and hypothesized relationships among the constructs. It is found that project facilities, location and communication, physical quality and prices have significant impact on customers’ buying attitude except the environmental issues and promotion. It is also found that buying intention is strongly influenced by buying attitude of the customers. The proposed model also has an acceptable fit to the data. Real Estate developers, marketers, policy makers can use the findings to better understand, segment and satisfy the customers. Therefore the findings of the study will definitely help in building customer based brand equity and customer loyalty particularly in Real Estate (Apartment Market)  to gain competitive advantages as well as achieve sustainable development of the sector. The study may be limited by its focus on a geographic section of the Bangladeshi Real Estate market.  Keywords: Buyers’ attitude, Buying intention, Buying intention model, Real estate, Real estate marketing

Numerical Solutions to Some Families of Fractional Order Differential Equations by Laguerre Polynomials

This article is devoted to compute numerical solutions of some classes and families of fractional order differential equations (FODEs). For the required numerical analysis, we utilize Laguerre polynomials and establish some operational matrices regarding to fractional order derivatives and integrals without discretizing the data. Further corresponding to boundary value problems (BVPs), we establish a new operational matrix which is used to compute numerical solutions of boundary value problems (BVPs) of FODEs. Based on these operational matrices (OMs), we convert the proposed (FODEs) or their system to corresponding algebraic equation of Sylvester type or system of Sylvester type. The resulting algebraic equations are solved by MATLAB® using Gauss elimination method for the unknown coefficient matrix. To demonstrate the suggested scheme for numerical solution, many suitable examples are provided

Malaysia as a Film Location for Foreign Production

The foreign film industry is one of the creative industries that has helped a lot to generate the country's economy and improve the tourism sector. The arrival of foreign film production can enhance the country's reputation through the introduction of science and culture to the world community through film. In addition, the creative industry is able to introduce interesting places in Malaysia to be used as filming locations. Indirectly can promote Malaysia as a destination of choice for filming purposes. In addition to helping promote the country, job opportunities can be created for artists and behind -the -scenes crew. Various factors must be identified as to why foreign production companies make Malaysia one of their filming locations whether in the category of films, drama series, documentaries or television programs. This study aims to identify the focus location for the purpose of filming foreign films and also look at the attractions and facilities such as incentives provided by the government to the production of these foreign films for filming in Malaysia. Keywords: foreign film filming locations, attractions, incentive facilities eISSN: 2398-4287© 2022. The Authors. Published for AMER ABRA cE-Bs by e-International Publishing House, Ltd., UK. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer–review under responsibility of AMER (Association of Malaysian Environment-Behaviour Researchers), ABRA (Association of Behavioural Researchers on Asians/Africans/Arabians) and cE-Bs (Centre for Environment-Behaviour Studies), Faculty of Architecture, Planning & Surveying, Universiti Teknologi MARA, Malaysia. DO

Review: Tea Tree (Melaleuca Alternifolia) As A New Material For Biocomposites

Melaleuca alternifolia or commonly known as tea tree is a tall shrub or small tree in the plant genus Melaleuca. It is popular for its oil, which is tea tree oil where it has been employed largely in various industries of its antimicrobial properties. Research works are still ongoing mainly focusing on the tea tree oil properties, ultimately almost none of them investigating on the residue which is the leaves. Environmental issues become the world major concern, which create awareness among industrial player to turn back to natural fibre in producing products. In recent time, productions of composites from agro waste have received considerable attention. This paper aims to rationalize the potential of tea tree (Melaleuca alternifolia) leaves as a new source of natural fibres or material in order to become the potential filler or reinforcer in the development of a new biocomposite

Application of Topological Degree Method for Solutions of Coupled Systems of Multipoints Boundary Value Problems of Fractional Order Hybrid Differential Equations

We established the theory to coupled systems of multipoints boundary value problems of fractional order hybrid differential equations with nonlinear perturbations of second type involving Caputo fractional derivative. The proposed problem is as follows: D cαxt-ft,xt=gt,yt,Iαyt, t∈J=[0,1],D cαyt-ft,yt=gt,xt,Iαxt, t∈J=0,1, D cpx0=ψxη1, x′0=0,…,xn-20=0, D cpx1=ψxη2, D cpy0=ψyη1, y′0=0,…,yn-20=0, D cpy1=ψyη2, where p,η1,η2∈0,1, ψ is linear, D cα is Caputo fractional derivative of order α, with n-1<α≤n, n∈N, and Iα is fractional integral of order α. The nonlinear functions f, g are continuous. For obtaining sufficient conditions on existence and uniqueness of positive solutions to the above system, we used the technique of topological degree theory. Finally, we illustrated the main results by a concrete example