Topics in Fractional Differential Equations is devoted to the existence and uniqueness of solutions for various classes of Darboux problems for hyperbolic differential equations or inclusions involving the Caputo fractional derivative. Fractional calculus generalizes the integrals and derivatives to non-integer orders. During the last decade, fractional calculus was found to play a fundamental role in the modeling of a considerable number of phenomena; in particular the modeling of memory-dependent and complex media such as porous media. It has emerged as an important tool for the study of dynamical systems where classical methods reveal strong limitations. Some equations present delays which may be finite, infinite, or state-dependent. Others are subject to an impulsive effect. The above problems are studied using the fixed point approach, the method of upper and lower solution, and the Kuratowski measure of noncompactness. This book is addressed to a wide audience of specialists such as mathematicians, engineers, biologists, and physicists.
Table des matières
Preface.- 1. Preliminary Background.- 2. Partial Hyperbolic Functional Differential Equations.- 3. Partial Hyperbolic Functional Differential Inclusions.- 4. Impulsive Partial Hyperbolic Functional Differential Equations.- 5. Impulsive Partial Hyperbolic Functional Differential Inclusions.- 6. Implicit Partial Hyperbolic Functional Differential Equations.- 7. Fractional Order Riemann-Liouville Integral Equations.- References.- Index.
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