{"product_id":"theory-and-methods-of-piecewise-defined-fractional-operators","title":"Theory and Methods of Piecewise Defined Fractional Operators","description":"\u003ci\u003eTheory and Methods of Piecewise Defined Fractional Operators\u003c\/i\u003eintroduces new mathematical methods to derive complex modeling solutions with stability, consistency, and convergence. These tools include new types of non-local derivatives and integrals, such as fractal-fractional derivatives and integrals. Drs. Atangana and Araz present the theoretical and numerical analyses of the newly introduced piecewise differential and integral operators where crossover behaviors are observed, as well as their applications to real-world problems. The book contains foundational concepts that will help readers better understand piecewise differential and integral calculus and their applications to modeling processes with crossover behaviors. Several Cauchy problems with piecewise differential operators are considered, and their existence and uniqueness under some conditions are presented; in particular, the Carathéodory principle is used to ensure the existence and uniqueness of these new Cauchy problems. New numerical schemes are introduced to derive numerical solutions to these new equations, and the stability, consistency, and convergence analysis of these new numerical approaches are also presented.\u003cbr\u003e\u003cbr\u003e\u003cul\u003e\n\u003cli\u003eProvides in-depth explanation of differential equations with fractional and piecewise differential and integral operators\u003c\/li\u003e\n\u003cli\u003eHelps readers understand why the concept of piecewise calculus is needed\u003c\/li\u003e\n\u003cli\u003eIncludes definitions of derivatives and integrals with their different properties\u003c\/li\u003e\n\u003cli\u003ePresents theoretical and numerical analyses of newly introduced piecewise\u003c\/li\u003e\n\u003cli\u003eCovers differential and integral operators where crossover behaviors are observed\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"None","offers":[{"title":"Paperback","offer_id":46560662094034,"sku":"9780443221569","price":266.5,"currency_code":"CAD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0655\/8980\/5233\/files\/1_3ce34161-bab7-4d8e-bc70-c8a0a247ded2.jpg?v=1762640000","url":"https:\/\/www.indigo.ca\/products\/theory-and-methods-of-piecewise-defined-fractional-operators","provider":"Indigo","version":"1.0","type":"link"}