<p>This book focuses on the recent development of fractional differential equations, integro-differential equations, and inclusions and inequalities involving the Hadamard derivative and integral. Through a comprehensive study based in part on their recent research, the authors address the issues related to initial and boundary value problems involving Hadamard type differential equations and inclusions as well as their functional counterparts. The book covers fundamental concepts of multivalued analysis and introduces a new class of mixed initial value problems involving the Hadamard derivative and Riemann-Liouville fractional integrals. In later chapters, the authors discuss nonlinear Langevin equations as well as coupled systems of Langevin equations with fractional integral conditions. Focused and thorough, this book is a useful resource for readers and researchers interested in the area of fractional calculus.<br></p>

Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities

Science & Math

Aḥmad, Bashīr

Alsaedi, Ahmed

Ntouyas, Sotiris K.

TARIBOON, JESSADA

Mathematics

Springer

This book focuses on the recent development of fractional differential equations, integro-differential equations, and inclusions and inequalities involving the Hadamard derivative and integral. Through a comprehensive study based in part on their recent research, the authors address the issues related to initial and boundary value problems involving Hadamard type differential equations and inclusions as well as their functional counterparts. The book covers fundamental concepts of multivalued analysis and introduces a new class of mixed initial value problems involving the Hadamard derivative and Riemann-Liouville fractional integrals. In later chapters, the authors discuss nonlinear Langevin equations as well as coupled systems of Langevin equations with fractional integral conditions. Focused and thorough, this book is a useful resource for readers and researchers interested in the area of fractional calculus.

This book derives an explicit analytical pattern (or framework) that permits the examination and optimization of biogas production systems. It provides a concise overview of the current status of biogas and biogas coupled agricultural systems in China, and introduces evaluation methods for energy efficiency, environmental emissions, economic performance and sustainability assessment approaches. Based on empirical studies, it also explores future options for the system development by focusing on emissions mitigation, biogas energy efficiency and system sustainability. Systematic methods of life cycle assessment and thermodynamic analysis may provide new angles for biogas system evaluation. The system discussed is not only a biogas producer, but also a biogas-linked ecological agricultural system, which has the potential to broaden the applicable scopes of renewable energy and eco-agricultural management. The comprehensive, in-depth knowledge and experience presented provide new analytical approaches for researchers in relevant fields and shed light on the construction and operation of emerging anaerobic digestion and biogas industries. This book is a valuable resource for researchers focusing on biogas system modeling, project managers and policymakers.

Biogas Systems in China

Business & Money

Chen, Bin

Hayat, Tasawar

Economics

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