Abdon Atangana - Derivative with a New Parameter : Theory, Methods and Applications read EPUB, TXT, PDF
9780128038253 English 012803825X Derivative with a New Parameter, Derivative with a New Parameter: Theory, Methods and Applications discusses the first application of the local derivative that was done by Newton for general physics, and later for other areas of the sciences. The book starts off by giving a history of derivatives, from Newton to Caputo. It then goes on to introduce the new parameters for the local derivative, including its definition and properties. Additional topics define beta-Laplace transforms, beta-Sumudu transforms, and beta-Fourier transforms, including their properties, and then go on to describe the method for partial differential with the beta derivatives. Subsequent sections give examples on how local derivatives with a new parameter can be used to model different applications, such as groundwater flow and different diseases. The book gives an introduction to the newly-established local derivative with new parameters, along with their integral transforms and applications, also including great examples on how it can be used in epidemiology and groundwater studies. Introduce the new parameters for the local derivative, including its definition and properties Provides examples on how local derivatives with a new parameter can be used to model different applications, such as groundwater flow and different diseases Includes definitions of beta-Laplace transforms, beta-Sumudu transforms, and beta-Fourier transforms, their properties, and methods for partial differential using beta derivatives Explains how the new parameter can be used in multiple methods, The first application of the local derivative was done by Newton for general physics and later on in other areas of sciences. However the local derivative was not able to explain some complex physical problems. Therefore fractional calculus and fractional order models were studied to try and solve these problems. There were further problems with fractional derivatives such as they do not obey some classical properties of calculus. Therefore a new derivative was introduced and called beta-derivative. The book starts off by giving a history of derivatives, from Newton to Caputo. It then goes onto introduce the new parameter for the local derivative, including the definition and properties. Another part of the book defines beta-Laplace transforms, beta-Sumudu transforms and beta-Fourier transforms and gives the properties of them. It then goes onto describe the method for partial differential with the beta derivative. It then ends with giving examples of how local derivative with a new parameter can be used to model different applications, such as groundwater flow and different diseases. Derivative with a new parameter gives an introduction to the newly-established local derivative with new parameters together with theirs integral transforms and their applications. It gives great examples of how it can be used in epidemiology and groundwater studies. Introduces the new parameter of the local derivative Explains how the new parameter can be used in multiple methods Discusses different applications, such as modelling of different, The notion of variation is used the build the differential equations, the derivative usually employed in this study is the version provided by Newton called the local derivative. The first application of this derivative was done by Newton for general physic and later on in other field of sciences. However, due to the complexity of physical problem encountered, this local derivative was not able to explain these complexities; the notion of derivative has been tailored. For example in order to specifically repeat the nonlocal, frequency- and history-dependent properties of power law observables fact, some diverse modeling apparatus supported by fractional operators have to be pioneered. Particularly, the compensation of fractional calculus and fractional order models meaning, differential systems involving fractional order integro-differential operators and their applications have previously been intensively studied throughout the last few decades with outstanding results. Also, the long-range temporal or spatial dependence observables fact intrinsic to the fractional order systems present unique peculiarity not supported by their integer order counterpart, which permit better models of the dynamics of complex processes. But the problem face with these fractional derivatives is that, they do not obey some classical properties of calculus that are being taught to undergrad students for instance there is no clear formula for the product of two functions, neither for the quotient of two functions, not to mention the composite of two functions. Another problem with these fractional derivatives is that, we cannot say clear anything about the behavior of the function, if the fractional derivative of this one is positive or negative. In order to take into account the properties of the classical calculus together with the concept of fractional order, a new derivative was introduced and called beta-derivative. Introduces the new parameter of the local derivative Explains how the new parameter can be used in multiple methods Discusses different applications, such as modelling of different
9780128038253 English 012803825X Derivative with a New Parameter, Derivative with a New Parameter: Theory, Methods and Applications discusses the first application of the local derivative that was done by Newton for general physics, and later for other areas of the sciences. The book starts off by giving a history of derivatives, from Newton to Caputo. It then goes on to introduce the new parameters for the local derivative, including its definition and properties. Additional topics define beta-Laplace transforms, beta-Sumudu transforms, and beta-Fourier transforms, including their properties, and then go on to describe the method for partial differential with the beta derivatives. Subsequent sections give examples on how local derivatives with a new parameter can be used to model different applications, such as groundwater flow and different diseases. The book gives an introduction to the newly-established local derivative with new parameters, along with their integral transforms and applications, also including great examples on how it can be used in epidemiology and groundwater studies. Introduce the new parameters for the local derivative, including its definition and properties Provides examples on how local derivatives with a new parameter can be used to model different applications, such as groundwater flow and different diseases Includes definitions of beta-Laplace transforms, beta-Sumudu transforms, and beta-Fourier transforms, their properties, and methods for partial differential using beta derivatives Explains how the new parameter can be used in multiple methods, The first application of the local derivative was done by Newton for general physics and later on in other areas of sciences. However the local derivative was not able to explain some complex physical problems. Therefore fractional calculus and fractional order models were studied to try and solve these problems. There were further problems with fractional derivatives such as they do not obey some classical properties of calculus. Therefore a new derivative was introduced and called beta-derivative. The book starts off by giving a history of derivatives, from Newton to Caputo. It then goes onto introduce the new parameter for the local derivative, including the definition and properties. Another part of the book defines beta-Laplace transforms, beta-Sumudu transforms and beta-Fourier transforms and gives the properties of them. It then goes onto describe the method for partial differential with the beta derivative. It then ends with giving examples of how local derivative with a new parameter can be used to model different applications, such as groundwater flow and different diseases. Derivative with a new parameter gives an introduction to the newly-established local derivative with new parameters together with theirs integral transforms and their applications. It gives great examples of how it can be used in epidemiology and groundwater studies. Introduces the new parameter of the local derivative Explains how the new parameter can be used in multiple methods Discusses different applications, such as modelling of different, The notion of variation is used the build the differential equations, the derivative usually employed in this study is the version provided by Newton called the local derivative. The first application of this derivative was done by Newton for general physic and later on in other field of sciences. However, due to the complexity of physical problem encountered, this local derivative was not able to explain these complexities; the notion of derivative has been tailored. For example in order to specifically repeat the nonlocal, frequency- and history-dependent properties of power law observables fact, some diverse modeling apparatus supported by fractional operators have to be pioneered. Particularly, the compensation of fractional calculus and fractional order models meaning, differential systems involving fractional order integro-differential operators and their applications have previously been intensively studied throughout the last few decades with outstanding results. Also, the long-range temporal or spatial dependence observables fact intrinsic to the fractional order systems present unique peculiarity not supported by their integer order counterpart, which permit better models of the dynamics of complex processes. But the problem face with these fractional derivatives is that, they do not obey some classical properties of calculus that are being taught to undergrad students for instance there is no clear formula for the product of two functions, neither for the quotient of two functions, not to mention the composite of two functions. Another problem with these fractional derivatives is that, we cannot say clear anything about the behavior of the function, if the fractional derivative of this one is positive or negative. In order to take into account the properties of the classical calculus together with the concept of fractional order, a new derivative was introduced and called beta-derivative. Introduces the new parameter of the local derivative Explains how the new parameter can be used in multiple methods Discusses different applications, such as modelling of different