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Preface 1 Introduction 1.1 Historical Development of Finsler Geometry 1.2 The Geometry of Finsler Spaces 1.3 Review of Literature about Finsler Geometry 1.4 Connections and Covariant Differentiations 1.5 Flag curvature and S-curvature in Finsler geometry 1.6 Some special Finsler spaces 1.7 KCC theory 1.8 Mathematical Cosmology in Finslerian space-time 2 On Finsler space with a special (¦Á, ¦Â)-metric 2.1 Introduction 2.2 The condition to be a Berwald space 2.3 The condition to be a Douglas space 2.4 The condition to be a Weakly-Berwald space 3 On Randers change of a Finsler space with m-th root metric 3.1 Introduction 3.2 Preliminaries 3.3 Fundamental metric tensor of Randers transformed m-th root metric 3.4 Spray coefficients of Randers transformed m-th root metric 3.5 Conformally related Randers transformed m-th root metric 3.6 Locally dually flatness of Randers transformed m-th root metric 4 On Conformal Transformation of m-th root Finsler metric 4.1 Introduction 4.2 Preliminaries 4.3 Fundamental tensor and Spray coefficients of conformally trans-formed m-th root metric 4.4 Locally dually flat conformally transformed m-th root metric 4.5 Conformally transformed Einstein m-th root metric 4.6 Conformally transformed m-th root metric with Isotropic E-curvature 5 Transformation of a Finsler Space by Normalised Semi-Parallel Vector Fields 5.1 Introduction 5.2 Transformed Finsler space obtained by Normalised semi-parallel vector fields 5.3 Special Finsler spaces with semi-parallel vector fields 6 Predator-prey model with prey refuges: Jacobi stability vs Linear stability 6.1 Introduction 6.2 Preliminary 6.3 Applications of geometric theory to second order system 6.4 Mathematical models 6.5 Numerical simulations and discussion 6.6 Conclusions 7 Finsler-Randers Cosmological models in Modified Gravity Theories 7.1 Introduction 7.2 Finsler-Randers Cosmological Model in Einstein Theory 7.3 Fiusler-Randers cosmological model in Lyra geometry 7.4 Finsler-Randers Cosmological Model in General Class of Scalar-tensor theory 7.5 Finsler-Randers Cosmological Model in C-field theory 7.6 Conclusions Bibliography ±à¼­ÊÖ¼Ç