On One Geoinformation Fractional Differential Model of the Variable Order

AbstractIn this manuscript, we examine both the existence and the stability of solutions to the implicit boundary value problem of Caputo fractional differential equations of variable order. We construct an example to illustrate the validity of the observed results.

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A predator–prey model involving variable-order fractional differential equations with Mittag-Leffler kernel

Advances in Difference Equations ◽

10.1186/s13662-021-03340-w ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Aziz Khan ◽

Hashim M. Alshehri ◽

J. F. Gómez-Aguilar ◽

Zareen A. Khan ◽

G. Fernández-Anaya

Keyword(s):

Fractional Order ◽

Existence And Uniqueness ◽

Variable Order ◽

Fractional Order Systems ◽

New Approach ◽

Predator Prey ◽

Predator Prey Model ◽

Prey Model ◽

Fractional Differential ◽

The Fixed Point Theorem

AbstractThis paper is about to formulate a design of predator–prey model with constant and time fractional variable order. The predator and prey act as agents in an ecosystem in this simulation. We focus on a time fractional order Atangana–Baleanu operator in the sense of Liouville–Caputo. Due to the nonlocality of the method, the predator–prey model is generated by using another FO derivative developed as a kernel based on the generalized Mittag-Leffler function. Two fractional-order systems are assumed, with and without delay. For the numerical solution of the models, we not only employ the Adams–Bashforth–Moulton method but also explore the existence and uniqueness of these schemes. We use the fixed point theorem which is useful in describing the existence of a new approach with a particular set of solutions. For the illustration, several numerical examples are added to the paper to show the effectiveness of the numerical method.

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Analytic approximate solutions for a class of variable order fractional differential equations using the polynomial least squares method

Fractional Calculus and Applied Analysis ◽

10.1515/fca-2017-0054 ◽

2017 ◽

Vol 20 (4) ◽

Cited By ~ 6

Author(s):

Constantin Bota ◽

Bogdan Căruntu

Keyword(s):

Differential Equations ◽

Least Squares ◽

Fractional Differential Equations ◽

Least Squares Method ◽

Approximate Solutions ◽

Variable Order ◽

Polynomial Solutions ◽

Fractional Differential ◽

Approximate Polynomial

AbstractIn this paper a new way to compute analytic approximate polynomial solutions for a class of nonlinear variable order fractional differential equations is proposed, based on the Polynomial Least Squares Method (PLSM). In order to emphasize the accuracy and the efficiency of the method several examples are included.

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New Operational Matrix for Solving Multiterm Variable Order Fractional Differential Equations

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4037922 ◽

2017 ◽

Vol 13 (1) ◽

Cited By ~ 8

Author(s):

A. M. Nagy ◽

N. H. Sweilam ◽

Adel A. El-Sayed

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Algebraic System ◽

Order Differential Equation ◽

Fundamental Problem ◽

Operational Matrix ◽

Variable Order ◽

Engineering Problems ◽

Fractional Differential ◽

Fourth Kind

The multiterm fractional variable-order differential equation has a massive application in physics and engineering problems. Therefore, a numerical method is presented to solve a class of variable order fractional differential equations (FDEs) based on an operational matrix of shifted Chebyshev polynomials of the fourth kind. Utilizing the constructed operational matrix, the fundamental problem is reduced to an algebraic system of equations which can be solved numerically. The error estimate of the proposed method is studied. Finally, the accuracy, applicability, and validity of the suggested method are illustrated through several examples.

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