Analysis of projectile motion in view of conformable derivative

Abstract This paper presents new solutions for twodimensional projectile motion in a free and resistive medium, obtained within the newly established conformable derivative. For free motion, we obtain analytical solutions and show that the trajectory, height, flight time, optimal angle, and maximum range depend on the order of the conformable derivative, 0 < γ ≤ 1. Likewise, we analyse and simulate the projectile motion in a resistive medium by assuming several scenarios. The obtained trajectories never exceed the ordinary ones, given by γ = 1, unlike results reported in other studies.

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Analytical Solutions of Fuzzy Linear Differential Equations in the Conformable Setting

Journal of Fractional Calculus and Nonlinear Systems ◽

10.48185/jfcns.v2i2.342 ◽

2021 ◽

Vol 2 (2) ◽

pp. 13-30

Author(s):

Awais Younus ◽

Muhammad Asif ◽

Usama Atta ◽

Tehmina Bashir ◽

Thabet Abdeljawad

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Ordinary Differential Equations ◽

Analytical Solutions ◽

Higher Order ◽

Linear Differential Equations ◽

Conformable Derivative ◽

Systems Of Differential Equations ◽

Two Systems ◽

Linear Differential

In this paper, we provide the generalization of two predefined concepts under the name fuzzy conformable differential equations. We solve the fuzzy conformable ordinary differential equations under the strongly generalized conformable derivative. For the order $\Psi$, we use two methods. The first technique is to resolve a fuzzy conformable differential equation into two systems of differential equations according to the two types of derivatives. The second method solves fuzzy conformable differential equations of order $\Psi$ by a variation of the constant formula. Moreover, we generalize our results to solve fuzzy conformable ordinary differential equations of a higher order. Further, we provide some examples in each section for the sake of demonstration of our results.

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Exact analytical solutions of the fractional biological population model, fractional EW and modified EW equations

An International Journal of Optimization and Control Theories & Applications (IJOCTA) ◽

10.11121/ijocta.01.2021.00841 ◽

2020 ◽

Vol 11 (1) ◽

pp. 52-58

Author(s):

Meryem Odabaşı

Keyword(s):

Analytical Solutions ◽

Population Model ◽

Traveling Wave Solutions ◽

Conformable Derivative ◽

Derivative Operator ◽

Trial Solution ◽

Exact Analytical Solutions ◽

Biological Population ◽

All Solutions ◽

Package Program

In this paper, exact analytical solutions of the biological population model, the EW and the modified EW equations with a conformable derivative operator have been examined by means of the trial solution algorithm and the complete discrimination system. Dark, bright and singular traveling wave solutions of the equations have been obtained by algorithm. Also, revealed singular periodic solutions have been listed. All solutions were verified by substituting them into their corresponding equation via Mathematica package program.

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Analytical Solutions for the Nonlinear Partial Differential Equations Using the Conformable Triple Laplace Transform Decomposition Method

International Journal of Differential Equations ◽

10.1155/2021/9988160 ◽

2021 ◽

Vol 2021 ◽

pp. 1-18

Author(s):

Shailesh A. Bhanotar ◽

Mohammed K. A. Kaabar

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Laplace Transform ◽

Analytical Solutions ◽

Decomposition Method ◽

Nonlinear Partial Differential Equations ◽

Three Dimensions ◽

Conformable Derivative ◽

Partial Differential ◽

Linear And Nonlinear

In this paper, a novel analytical method for solving nonlinear partial differential equations is studied. This method is known as triple Laplace transform decomposition method. This method is generalized in the sense of conformable derivative. Important results and theorems concerning this method are discussed. A new algorithm is proposed to solve linear and nonlinear partial differential equations in three dimensions. Moreover, some examples are provided to verify the performance of the proposed algorithm. This method presents a wide applicability to solve nonlinear partial differential equations in the sense of conformable derivative.

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On the Solutions of Fractional Cauchy Problem Featuring Conformable Derivative

ITM Web of Conferences ◽

10.1051/itmconf/20182201045 ◽

2018 ◽

Vol 22 ◽

pp. 01045 ◽

Cited By ~ 3

Author(s):

Mehmet Yavuz ◽

Necati Özdemir

Keyword(s):

Differential Equation ◽

Cauchy Problem ◽

Exact Solutions ◽

Detailed Analysis ◽

Analytical Solutions ◽

Homotopy Analysis Method ◽

Analysis Method ◽

Conformable Derivative ◽

Homotopy Analysis ◽

Fractional Cauchy Problem

In this study, we have obtained analytical solutions of fractional Cauchy problem by using q-Homotopy Analysis Method (q-HAM) featuring conformable derivative. We have considered different situations according to the homogeneity and linearity of the fractional Cauchy differential equation. A detailed analysis of the results obtained in the study has been reported. According to the results, we have found out that our obtained solutions approach very speedily to the exact solutions.

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Analytical construction of the projectile motion trajectory in midair

MOMENTO ◽

10.15446/mo.n62.90752 ◽

2021 ◽

pp. 79-96

Author(s):

Peter Chudinov ◽

Vladimir Eltyshev ◽

Yuri Barykin

Keyword(s):

Analytical Solutions ◽

Initial Conditions ◽

Resistance Force ◽

Tennis Ball ◽

Projectile Motion ◽

Classic Problem ◽

Analytical Construction ◽

Air Resistance ◽

Wide Range ◽

Large Period

A classic problem of the motion of a projectile thrown at an angle to the horizon is studied. Air resistance force is taken into account with the use of the quadratic resistance law. An analytic approach is mainly applied for the investigation. Equations of the projectile motion are solved analytically for an arbitrarily large period of time. The constructed analytical solutions are universal, that is, they can be used for any initial conditions of throwing. As a limit case of motion, the vertical asymptote formula is obtained. The value of the vertical asymptote is calculated directly from the initial conditions of motion. There is no need to study the problem numerically. The found analytical solutions are highly accurate over a wide range of parameters. The motion of a baseball, a tennis ball, and a shuttlecock of badminton are presented as examples.

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Approximate Analytical Solutions to Conformable Modified Burgers Equation Using Homotopy Analysis Method

Annales Mathematicae Silesianae ◽

10.2478/amsil-2018-0011 ◽

2019 ◽

Vol 33 (1) ◽

pp. 159-167 ◽

Cited By ~ 2

Author(s):

Ali Kurt ◽

Orkun Tasbozan

Keyword(s):

Analytical Solution ◽

Analytical Solutions ◽

Homotopy Analysis Method ◽

Burgers Equation ◽

Approximate Analytical Solution ◽

Analysis Method ◽

Conformable Derivative ◽

Modified Burgers Equation ◽

Approximate Analytical Solutions ◽

Homotopy Analysis

AbstractIn this paper the authors aspire to obtain the approximate analytical solution of Modified Burgers Equation with newly defined conformable derivative by employing homotopy analysis method (HAM).

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