Fractional Differential Equations

Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

Series Preface * Preface to the Third Edition * 1 Linear Systems * 2 Nonlinear Systems: Local Theory * 3 Nonlinear Systems: Global Theory * 4 Nonlinear Systems: Bifurcation Theory * References * Index

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Differential Equations and Dynamical Systems

Models in Ecology

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Encyclopedia of Quality of Life and Well-Being Research

In this paper, we obtain approximate bound state solutions of an N-dimensional fractional time independent Schrodinger equation for a generalised Mie-type potential, namely, V(rα)=Ar2α+Brα+C. Here α(0 < α < 1) acts like a fractional parameter for the space variable r. When α = 1 the potential converts into the original form of Mie-type of potential that is generally studied in molecular and chemical physics. The entire study is composed with a Jumarie-type fractional derivative approach. The solution is expressed via the Mittag-Leffler function and fractionally defined confluent hypergeometric function. To ensure the validity of the present work, obtained results are verified with the previous studies for different potential parameter configurations, specially for α = 1. At the end, few numerical calculations for energy eigenvalue and bound state eigenfunctions are furnished for a typical diatomic molecule.

Time independent fractional Schrödinger equation for generalized Mie-type potential in higher dimension framed with Jumarie type fractional derivative

There is no unified method to solve the fractional differential equation. The type of derivative here used in this paper is of Jumarie formulation, for the several differential equations studied. Here we develop an algorithm to solve the linear fractional differential equation composed via Jumarie fractional derivative in terms of Mittag-Leffler function; and show its conjugation with ordinary calculus. In these fractional differential equations the one parameter Mittag-Leffler function plays the role similar as exponential function used in ordinary differential equations.

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Analytic Solution of Linear Fractional Differential Equation with Jumarie Derivative in Term of Mittag- Leffler Function

Studies of different types of bifurcations analyses of an imprecise two species food chain model with fear effect and non-linear harvesting

Mathematical modelling of COVID-19: A case study of Italy

In this paper, we have considered a deterministic epidemic model with logistic growth rate of the susceptible population, non-monotone incidence rate, nonlinear treatment function with impact of limited hospital beds and performed control strategies. The existence and stability of equilibria as well as persistence and extinction of the infection have been studied here. We have investigated different types of bifurcations, namely Transcritical bifurcation, Backward bifurcation, Saddle-node bifurcation and Hopf bifurcation, at different equilibrium points under some parametric restrictions. Numerical simulation for each of the above-defined bifurcations shows the complex dynamical phenomenon of the infectious disease. Furthermore, optimal control strategies are performed using Pontryagin's maximum principle and strategies of controls are studied for two infectious diseases. Lastly using efficiency analysis we have found the effective control strategies for both cases.

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Uttam Ghosh

Papers

Time independent fractional Schrödinger equation for generalized Mie-type potential in higher dimension framed with Jumarie type fractional derivative

Analytic Solution of Linear Fractional Differential Equation with Jumarie Derivative in Term of Mittag- Leffler Function

Studies of different types of bifurcations analyses of an imprecise two species food chain model with fear effect and non-linear harvesting

Mathematical modelling of COVID-19: A case study of Italy

Global dynamics and control strategies of an epidemic model having logistic growth, non-monotone incidence with the impact of limited hospital beds