Q fractional calculus and equations pdf files

This ninechapter monograph introduces a rigorous investigation of q difference operators in standard and fractional settings. The multiplicity solutions for nonlinear fractional differential. Fractional calculus fc started with the ideas of gottfried leibniz by the end of the xvii century. The fractional calculus may be considered an old and yet novel topic. A note on hadamard fractional differential equations with varying coefficients and their. The term fractional is a misnomer, but it is retained following the prevailing use. Pdf study of new class of qfractional derivative and its properties. Generalized qfractional difference operator was defined in the aid of. Fractional calculus is the branch of calculus that generalizes the derivative of a function to noninteger order, allowing calculations such as deriving a function to 12 order. Despite generalized would be a better option, the name fractional is used for denoting this kind of derivative. Our analysis, based on the classical linear theory of viscoelsticity recalled in chapter 2, will start from the power law creep to. Annaby and others published qfractional calculus and equations find, read and cite all the research you need on researchgate. Fractional viscoelastic models linear viscoelasticity is certainly the eld of the most extensive applications of fractional calculus, in view of its ability to model hereditary phenomena with long memory. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with.

Mathematical modeling with multidisciplinary applications details the interdisciplinary nature of mathematical modeling and numerical algorithms. It starts with elementary calculus of qdifferences and integration of jacksons type. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Fractional derivatives and integrals are convolutions with a power law. Annaby and others published q fractional calculus and equations find, read and cite all the research you need.

Features mathematical modeling techniques and realworld processes with applications in diverse fields. The existence and uniqueness theorems are derived using successive approximations, leading to systems of equations with retarded arguments. In this work, we considered the qdifferential equations of order 0 q fractional order considered here is the caputo time since it allows the use of initial conditions. An introduction to the fractional calculus and fractional differential equations book. The number of studies in this field has increased after 1930, when e. In this work, we considered the qdifferential equations of order 0 fractional calculus. An introduction to the fractional calculus and fractional. An analytical method to obtain exact solution of this class of fractional differential equations is provided. The fractional derivative was introduced in 1695 by leibnitz as a generalization of the integer order derivative and was reconsidered also by euler, abel, riemann liouville, grunwald and letnikov. Fractional calculus is a branch of mathematical analysis that studies the possibility of taking real number powers or complex number powers of the differentiation and integration operators. As in the classical theory of ordinary fractional differential equations, qdifference equations of fractional order are divided into linear, nonlinear, homogeneous, and inhomogeneous equations with constant and variable coefficients.