Fixed Point Theory and Fractional Calculus: Recent Advances and Applications (Forum for Interdisciplinary Mathematics)

Preface
Contents
About the Editors
Best Proximity Points for Some Multivalued Contractive Mappings
	1 Introduction
	2 Best Proximity Point for MVFC
	3 Conclusion
	References
Best Proximity Point Theorems via Some Generalized Notions
	1 Introduction
	2 Preliminaries
	3 Best Proximity Results for mathcalZ-Contraction and Its Generalizations
	4 Best Proximity Results in Some Other Generalized Contractions
	5 Example
	References
New Fixed-Figure Results on Metric Spaces
	1 Introduction
	2 Main Results
		2.1 Fixed-Circle Theorems and Related Consequences
		2.2 Fixed-Ellipse Theorems and Related Consequences
		2.3 Fixed-Hyperbola Theorems and Related Consequences
		2.4 Fixed-Cassini Curve Theorems and Related Consequences
		2.5 Fixed-Apollonius Circle Theorems and Related Consequences
		2.6 Some Illustrative Examples
	3 Conclusion
	References
Some Fixed Point Results for Suzuki W-Contractions Involving Quadratic Terms in Modular b-Metric Spaces
	1 Introduction and Preliminaries
	2 Main Results
	3 Examples
	4 Conclusion
	References
Some Common Fixed Point Results via α-Series for a Family of JS-Contraction Type Mappings
	1 Introduction
	2 Main Results
	3 Application
	References
Solution of Nonlinear First-Order Hybrid Integro-Differential Equations via Fixed Point Theorem
	1 Introduction
	2 Preliminaries
	3 Main Results
	4 Application to a Nonlinear First-Order Hybrid Integro-Differential Equations
	References
Application of Darbo's Fixed Point Theorem for Existence Result of Generalized 2D Functional Integral Equations
	1 Introduction
	2 Preliminaries
	3 Main Results
	4 Applications
	5 Conclusion
	References
Results on Generalized Tripled Fuzzy b-Metric Spaces
	1 Introduction
	2 Some Definition
	3 Major Work of the Chapter
		3.1 Definition and Example of TFbMS
		3.2 Some Results in TFbMS
		3.3 Fixed Point and Related Proposition in TFbMS
	4 Conclusion
	References
A Novel Controlled Picture Fuzzy Metric Space and Some Related Fixed Point Results
	1 Introduction
	2 Preliminaries
	3 Main Results
	4 Application to Fuzzy Fredholm Integral Equation
	References
Theoretical Analysis for a Generalized Fractional-Order Boundary Value Problem
	1 Introduction
	2 Preliminaries and Theoretical Results
	3 Main Results
		3.1 Existence Result
		3.2 Uniqueness Result
	4 Concluding Remarks
	References
On Well-posed Variational Problems Involving Multidimensional Integral Functionals
	1 Introduction
	2 Preliminaries
	3 Well-Posedness Associated with (CVIP)
	4 Well-Posedness in Generalized Sense Associated with (CVIP)
	5 Conclusions
	References
On the Coupled System of Tempered Fractional Differential Equations with Anti-periodic Boundary Conditions
	1 Introduction
	2 An Auxiliary Lemma
	3 Main Results
	4 Examples
	References
Application of Measure of Noncompactness on the Infinite System of Hadamard Fractional Integral Equations
	1 Introduction
	2 Application of MNC on Infinite System of Hadamard Fractional Integral Equations
	3 Existence of Solution on mathcalC(Z,c0)
	4 Existence of Solution on mathcalC(Z,ell1)
	5 Existence of Solution in mathcalC(Z,ellpα)
	References
Observability, Reachability, Trajectory Reachability and Optimal Reachability of Fractional Dynamical Systems using Riemann–Liouville Fractional Derivative
	1 Introduction
	2 Preliminaries
	3 Observability
	4 Reachability
	5 Trajectory—Reachability
	6 Optimal Reachability
	References
Fractional Calculus Approach to Logistic Equation and its Application
	1 Background of Study
	2 Preliminaries
		2.1 Mittag-Leffler Function
		2.2 Mittag-Leffler Function in Two Parameters
		2.3 Riemann–Liouville Fractional Derivative
		2.4 Caputo's Fractional Derivative
	3 Main Results
		3.1 Mittag-Leffler Function (Eα) as the Base for Logarithm Function
		3.2 Fractional Logistic Equation and Its Solution
	4 Mathematical Modeling
	5 Application in Epidemiology
		5.1 SI Model
		5.2 SIS Model
	6 Conclusion
	References
Hermite–Hadamard Type Inequalities for Coordinated Quasi-Convex Functions via Generalized Fractional Integrals
	1 Introduction
	2 Main Results
	3 Conclusion
	References
Leray–Schauder Theorem for Implicit Fractional Differential Equation and Nonlocal Multi-Point Conditions
	1 Introduction
	2 Background Materials
	3 Main Results
		3.1 Existence Result via Leray–Schauder Degree
		3.2 Existence and Uniqueness Result via Boyd and Wong Fixed Point Theorem
	4 Application
	5 Conclusions
	References
The q-Deformed Hamiltonian, Lagrangian, Entropy and Fisher Information
	1 Introduction
	2 The n-Parameter Generalised Hamiltonian and Lagrangian
		2.1 One-Parameter Hamiltonian
		2.2 One-Parameter Lagrangian
		2.3 Lagrangian and Hamiltonian Hierarchies
		2.4 Two-Parameter Hamiltonian
		2.5 Two-Parameter Lagrangian
		2.6 n-Parameter Hamiltonian and Lagrangian
	3 Generalised Entropies
		3.1 Boltzmann–Gibbs Entropy
		3.2 Shannon Entropy
		3.3 Kullback–Leibler Divergence
		3.4 Rényi Entropy: One-Parameter Generalisation of the Shannon Entropy
		3.5 Tsallis Entropy: One-Parameter Generalisation of the Boltzmann–Gibbs Entropy
		3.6 Sharma–Mittal Entropy: Two-Parameter Generalisation of the Boltzmann–Gibbs Entropy
		3.7 Generalisation of the Kullback–Leibler Divergence
	4 Fisher Information and Its Generalisation
		4.1 Likelihood Function
		4.2 Fisher Information
		4.3 Cramér–Rao Inequality and Additivity
		4.4 Connection with the Action Functional
		4.5 One-Parameter Generalisation of the Fisher Information
		4.6 Generalisation of the Cramer–Rao Inequality and Additive Property
		4.7 Two-Parameter Generalised Fisher Information
	5 Concluding Summary
	References