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The topic of this book is the mathematical and numerical analysis of some recent frameworks based on differential equations and their application in the mathematical modeling of complex systems, especially of living matter. First, the recent new mathematical frameworks based on generalized kinetic theory, fractional calculus, inverse theory, Schrödinger equation, and Cahn–Hilliard systems are presented and mathematically analyzed. Specifically, the well-posedness of the related Cauchy problems is investigated, stability analysis is also performed (including the possibility to have Hopf bifurcations), and some optimal control problems are presented. Second, this book is concerned with the derivation of specific models within the previous mentioned frameworks and for complex systems in biology, epidemics, and engineering. This book is addressed to graduate students and applied mathematics researchers involved in the mathematical modeling of complex systems.

boundedness --- delay --- Hopf bifurcation --- Lyapunov functional --- stability --- SEIQRS-V model --- kinetic theory --- integro-differential equations --- complex systems --- evolution equations --- thermostat --- nonequilibrium stationary states --- discrete Fourier transform --- discrete kinetic theory --- nonlinearity --- fractional operators --- Cahn–Hilliard systems --- well-posedness --- regularity --- optimal control --- necessary optimality conditions --- Schrödinger equation --- Davydov’s model --- partial differential equations --- exact solutions --- fractional derivative --- abstract Cauchy problem --- C0−semigroup --- inverse problem --- active particles --- autoimmune disease --- degenerate equations --- real activity variable --- Cauchy problem --- electric circuit equations --- wardoski contraction --- almost (s, q)—Jaggi-type --- b—metric-like spaces --- second-order differential equations --- dynamical systems --- compartment model --- epidemics --- basic reproduction number

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In the past few decades, several interesting problems have been solved using fixed point theory. In addition to classical ordinary differential equations and integral equation, researchers also focus on fractional differential equations (FDE) and fractional integral equations (FIE). Indeed, FDE and FIE lead to a better understanding of several physical phenomena, which is why such differential equations have been highly appreciated and explored. We also note the importance of distinct abstract spaces, such as quasi-metric, b-metric, symmetric, partial metric, and dislocated metric. Sometimes, one of these spaces is more suitable for a particular application. Fixed point theory techniques in partial metric spaces have been used to solve classical problems of the semantic and domain theory of computer science. This book contains some very recent theoretical results related to some new types of contraction mappings defined in various types of spaces. There are also studies related to applications of the theoretical findings to mathematical models of specific problems, and their approximate computations. In this sense, this book will contribute to the area and provide directions for further developments in fixed point theory and its applications.

Research & information: general --- Mathematics & science --- common coupled fixed point --- bv(s)-metric space --- T-contraction --- weakly compatible mapping --- quasi-pseudometric --- start-point --- end-point --- fixed point --- weakly contractive --- variational inequalities --- inverse strongly monotone mappings --- demicontractive mappings --- fixed point problems --- Hadamard spaces --- geodesic space --- convex minimization problem --- resolvent --- common fixed point --- iterative scheme --- split feasibility problem --- null point problem --- generalized mixed equilibrium problem --- monotone mapping --- strong convergence --- Hilbert space --- the condition (ℰμ) --- standard three-step iteration algorithm --- uniformly convex Busemann space --- compatible maps --- common fixed points --- convex metric spaces --- q-starshaped --- fixed-point --- multivalued maps --- F-contraction --- directed graph --- metric space --- coupled fixed points --- cyclic maps --- uniformly convex Banach space --- error estimate --- equilibrium --- fixed points --- symmetric spaces --- binary relations --- T-transitivity --- regular spaces --- b-metric space --- b-metric-like spaces --- Cauchy sequence --- pre-metric space --- triangle inequality --- weakly uniformly strict contraction --- S-type tricyclic contraction --- metric spaces --- b2-metric space --- binary relation --- almost ℛg-Geraghty type contraction

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

In the past few decades, several interesting problems have been solved using fixed point theory. In addition to classical ordinary differential equations and integral equation, researchers also focus on fractional differential equations (FDE) and fractional integral equations (FIE). Indeed, FDE and FIE lead to a better understanding of several physical phenomena, which is why such differential equations have been highly appreciated and explored. We also note the importance of distinct abstract spaces, such as quasi-metric, b-metric, symmetric, partial metric, and dislocated metric. Sometimes, one of these spaces is more suitable for a particular application. Fixed point theory techniques in partial metric spaces have been used to solve classical problems of the semantic and domain theory of computer science. This book contains some very recent theoretical results related to some new types of contraction mappings defined in various types of spaces. There are also studies related to applications of the theoretical findings to mathematical models of specific problems, and their approximate computations. In this sense, this book will contribute to the area and provide directions for further developments in fixed point theory and its applications.

Research & information: general --- Mathematics & science --- common coupled fixed point --- bv(s)-metric space --- T-contraction --- weakly compatible mapping --- quasi-pseudometric --- start-point --- end-point --- fixed point --- weakly contractive --- variational inequalities --- inverse strongly monotone mappings --- demicontractive mappings --- fixed point problems --- Hadamard spaces --- geodesic space --- convex minimization problem --- resolvent --- common fixed point --- iterative scheme --- split feasibility problem --- null point problem --- generalized mixed equilibrium problem --- monotone mapping --- strong convergence --- Hilbert space --- the condition (ℰμ) --- standard three-step iteration algorithm --- uniformly convex Busemann space --- compatible maps --- common fixed points --- convex metric spaces --- q-starshaped --- fixed-point --- multivalued maps --- F-contraction --- directed graph --- metric space --- coupled fixed points --- cyclic maps --- uniformly convex Banach space --- error estimate --- equilibrium --- fixed points --- symmetric spaces --- binary relations --- T-transitivity --- regular spaces --- b-metric space --- b-metric-like spaces --- Cauchy sequence --- pre-metric space --- triangle inequality --- weakly uniformly strict contraction --- S-type tricyclic contraction --- metric spaces --- b2-metric space --- binary relation --- almost ℛg-Geraghty type contraction --- common coupled fixed point --- bv(s)-metric space --- T-contraction --- weakly compatible mapping --- quasi-pseudometric --- start-point --- end-point --- fixed point --- weakly contractive --- variational inequalities --- inverse strongly monotone mappings --- demicontractive mappings --- fixed point problems --- Hadamard spaces --- geodesic space --- convex minimization problem --- resolvent --- common fixed point --- iterative scheme --- split feasibility problem --- null point problem --- generalized mixed equilibrium problem --- monotone mapping --- strong convergence --- Hilbert space --- the condition (ℰμ) --- standard three-step iteration algorithm --- uniformly convex Busemann space --- compatible maps --- common fixed points --- convex metric spaces --- q-starshaped --- fixed-point --- multivalued maps --- F-contraction --- directed graph --- metric space --- coupled fixed points --- cyclic maps --- uniformly convex Banach space --- error estimate --- equilibrium --- fixed points --- symmetric spaces --- binary relations --- T-transitivity --- regular spaces --- b-metric space --- b-metric-like spaces --- Cauchy sequence --- pre-metric space --- triangle inequality --- weakly uniformly strict contraction --- S-type tricyclic contraction --- metric spaces --- b2-metric space --- binary relation --- almost ℛg-Geraghty type contraction