Topics in Fractional Differential Equations

1. Front Matter

   Pages i-xiii

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2. Introduction

   • Saïd Abbas, Mouffak Benchohra, Gaston M. N’Guérékata

   Pages 1-10

3. Preliminary Background

   • Saïd Abbas, Mouffak Benchohra, Gaston M. N’Guérékata

   Pages 11-24

4. Partial Hyperbolic Functional Differential Equations

   • Saïd Abbas, Mouffak Benchohra, Gaston M. N’Guérékata

   Pages 25-114

5. Partial Hyperbolic Functional Differential Inclusions

   • Saïd Abbas, Mouffak Benchohra, Gaston M. N’Guérékata

   Pages 115-169

6. Impulsive Partial Hyperbolic Functional Differential Equations

   • Saïd Abbas, Mouffak Benchohra, Gaston M. N’Guérékata

   Pages 171-249

7. Impulsive Partial Hyperbolic Functional Differential Inclusions

   • Saïd Abbas, Mouffak Benchohra, Gaston M. N’Guérékata

   Pages 251-285

8. Implicit Partial Hyperbolic Functional Differential Equations

   • Saïd Abbas, Mouffak Benchohra, Gaston M. N’Guérékata

   Pages 287-339

9. Fractional Order Riemann–Liouville Integral Equations

   • Saïd Abbas, Mouffak Benchohra, Gaston M. N’Guérékata

   Pages 341-382

10. Back Matter

    Pages 383-396

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​​​ 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. ​

• Caputo Fractional derivative
• Darboux problem
• Riemann-Liouville Integral equations
• fractional calculus
• fractional differential equations
• hyperbolic partial differential equation
• partial differential equations

• , Laboratoire de Mathématiques, Université de Saïda, Saïda, Algeria

  Saïd Abbas

• , Laboratoire de Mathématiques, Université de Sidi Bel-Abbès, Sidi Bel-Abbès, Algeria

  Mouffak Benchohra

• , Department of Mathematics, Morgan State University, Baltimore, USA

  Gaston M. N'Guérékata

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