http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
This book is a scholarly work that explores theoretical aspects and applications of fractional differential equations in complex systems. Edited by Praveen Agarwal and other contributors, it provides comprehensive coverage on the extension of M-fractional derivatives, properties of Apostol-type polynomials, and computational methods for solving fractional differential equations in physics and engineering. The book is intended for researchers, practitioners, and graduate students in applied mathematics and engineering, offering insights into advanced mathematical techniques and their practical applications.
6.3 Spline approximation method for a system of fractional differential equations -- 6.3.1 Error estimation and convergence analysis -- 6.3.2 Stability of the method -- 6.3.3 Numerical example of a system of fractional differential equations -- 6.4 Modified homotopy perturbation method for the fractional Bagley-Torvik equation -- 6.4.1 Different approaches towards new iterative methods -- 6.4.1.1 First approach -- 6.4.1.2 Second approach -- 6.4.2 One-Step New Iterative Method (OSNIM) -- 6.4.3 Convergence and error analysis -- 6.4.4 Illustrating examples -- 6.5 Conclusion -- References -- 7 A study on the properties of new generalized special functions, their integral transformations, and applications to fracti... -- 7.1 Introduction and preliminaries -- 7.2 New generalized special functions -- 7.3 Properties -- 7.4 Integral transforms -- 7.4.1 Beta transform -- 7.4.2 Mellin transform -- 7.4.3 Laplace transform -- 7.4.4 Sumudu transform -- 7.4.5 Elzaki transform -- 7.4.6 General integral transform -- 7.5 Solution of fractional differential equations -- 7.6 Conclusion -- References -- 8 Congruence between mild and classical solutions of generalized fractional impulsive evolution equation -- 8.1 Introduction and preliminaries -- 8.2 Mild solution -- 8.3 Classical solution -- 8.4 Congruence between classical and mild solutions -- References -- 9 Application of various methods to solve some fractional differential equations in different fields -- 9.1 Introduction -- 9.2 Preliminaries -- 9.3 Idea of the used methods -- 9.3.1 Analysis of the GMLFM -- 9.3.2 Analysis of the PCM -- 9.3.3 Analysis of the MGMLFM -- 9.3.4 Analysis of the LADM -- 9.4 Results and discussion -- 9.4.1 Fractional-order model of human liver -- 9.4.1.1 Qualitative analysis of the solution -- 9.4.1.2 Simulation results -- 9.4.2 Fractional dynamics of a predator-prey system.
9.4.2.1 Stability of the EPs -- 9.4.2.2 Implementing the MGMLFM and simulating the results -- 9.4.3 Fractional-order Broer-Kaup (BK) system -- 9.4.3.1 Implementation of proposed methods -- 9.4.3.2 Simulation of the results -- 9.4.4 Fractional-order Burgers' system -- 9.4.4.1 Implementation of proposed methods -- 9.4.4.2 Simulation of the results -- 9.5 Conclusion -- References -- 10 Modeling capillary absorption in building materials with emphasis on the fourth root time law: time-fractional models, so... -- 10.1 Introduction -- 10.1.1 Experimental background -- 10.1.2 Existing models -- 10.1.3 Aim -- 10.1.4 Main lines of development of this study -- 10.2 New approach: physical and modeling background -- 10.2.1 Mass balance of absorbing species -- 10.2.2 Sharp front diffusion approach -- 10.2.3 Integral-balance solution -- 10.3 Next study tasks -- 10.4 A variety of alternative models -- 10.4.1 Integer-order nonlinear diffusion models -- 10.4.1.1 Diffusion model with a power-law time-dependent diffusivity -- 10.4.1.2 Fourth-order diffusion model with a constant diffusivity -- 10.4.2 Fractional diffusion models -- 10.4.2.1 Fractional diffusion model 1: constant diffusivity -- 10.4.2.2 Fractional diffusion model 2: time-dependent diffusivity -- 10.4.2.3 Fractional diffusion model 3: concentration dependent (power-law) diffusivity -- 10.5 Some briefs and preliminarily analyses -- 10.5.1 Integer-order diffusion models -- 10.5.1.1 Integer-order diffusion model with a time-dependent diffusivity -- 10.5.1.2 Fourth-order diffusion model -- 10.5.2 Fraction diffusion models -- 10.5.2.1 Fractional diffusion model 1 -- 10.5.2.2 Fractional diffusion model 2 -- 10.5.2.3 Fractional diffusion model 3 -- 10.6 Tests with published data: does the 1/4 law is obeyed everywhere? -- 10.7 Concentration profiles: approximate solutions.
10.8 The parameter m and the exponent n in the nonlinear diffusion model: some suggestions -- 10.9 Conclusions -- Acknowledgments -- References -- 11 Fuzzy fractional Caputo-type numerical scheme for solving fuzzy nonlinear equations -- 11.1 Introduction -- 11.2 Construction of fuzzy fractional Newton-type numerical schemes -- 11.3 Numerical results -- 11.4 Conclusion -- References -- 12 Approximate solutions of epidemic model of Zika virus -- 12.1 Introduction -- 12.2 Preliminaries on fractional calculus -- 12.3 Mathematical model formulation -- 12.3.1 Classical integer model -- 12.3.2 Fractional order mathematical model -- 12.4 Basic properties of the model -- 12.4.1 Existence and uniqueness -- 12.4.2 Invariant region and attractivity -- 12.4.3 Positivity and boundedness -- 12.5 Analysis -- 12.5.1 Equilibrium analysis -- 12.5.2 Stability analysis -- 12.5.2.1 Stability of DFE point E0 -- 12.5.2.2 Stability of EE point E∗ -- 12.6 Numerical methods and simulations -- 12.7 Numerical simulation and sensitivity analysis -- 12.8 Convergence analysis -- 12.9 Discussion -- 12.10 Conclusion -- References -- 13 On the nonlocal boundary value problem for the coupled system -- 13.1 Introduction -- 13.2 Existence of solution -- 13.2.1 Integral condition -- 13.3 Uniqueness of solution -- 13.4 Continuous dependence -- 13.5 Both analytical and numerical approaches -- 13.5.1 The Adomian decomposition method -- 13.5.2 Numerical technique derivation -- 13.6 Numerical examples -- 13.7 Conclusion -- References -- 14 Solutions of nonlinear time fractional Klein-Gordon equations using composite fractional derivatives -- 14.1 Introduction -- 14.2 Basic tools -- 14.2.1 Fractional calculus -- 14.2.2 Generalized iterative method -- 14.3 Solution of nonlinear fractional Klein-Gordon equations with composite fractional derivatives -- 14.4 Applications -- 14.5 Conclusion.
Équations différentielles fractionnaires