Modeling Exponential Growth and Exponential Decay Real Phenomena by Ψ-Caputo Fractional Derivative

Awadalla, Muath; Yameni, Y. Y.

doi:10.9734/jamcs/2018/43054

Cited by 18 publications

(9 citation statements)

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“…In this section, we recall some notations, de nitions and preliminaries about fractional calculus [18][19][20], and -Caputo fractional calculus [4,17,[21][22][23].…”

Section: Preliminariesmentioning

confidence: 99%

Existence of Solutions for Anti-Periodic Fractional Differential Inclusions with ψ-Caupto Fractional Derivative

Yang

Bai

2019

Discrete Dynamics in Nature and Society

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In this paper, we investigate the existence of solutions for a class of fractional boundary value problems with anti-periodic boundary value conditions with ψ-Caupto fractional derivative. By means of some standard fixed point theorems, sufficient conditions for the existence of solutions for the fractional differential inclusions with ψ-Caputo derivatives are presented. Our result generalizes the known special case if ψx=x and single known results to the multi-valued ones.

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“…In this section, we recall some notations, de nitions and preliminaries about fractional calculus [18][19][20], and -Caputo fractional calculus [4,17,[21][22][23].…”

Section: Preliminariesmentioning

confidence: 99%

Existence of Solutions for Anti-Periodic Fractional Differential Inclusions with ψ-Caupto Fractional Derivative

Yang

Bai

2019

Discrete Dynamics in Nature and Society

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“…In this section, we recall some notation, definitions and preliminaries about fractional calculus [6,7,21], ψ-Caputo fractional calculus [3][4][5]22,23], and Riesz or Riesz-Caputo fractional derivative [17][18][19]. Definition 1 ([6]).…”

Section: Preliminariesmentioning

confidence: 99%

Existence of Solutions for Anti-Periodic Fractional Differential Inclusions Involving ψ-Riesz-Caputo Fractional Derivative

Yang

Bai

2019

Mathematics

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In this paper, we investigate the existence of solutions for a class of anti-periodic fractional differential inclusions with ψ -Riesz-Caputo fractional derivative. A new definition of ψ -Riesz-Caputo fractional derivative of order α is proposed. By means of Contractive map theorem and nonlinear alternative for Kakutani maps, sufficient conditions for the existence of solutions to the fractional differential inclusions are given. We present two examples to illustrate our main results.

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“…Evidence of fractional calculus being applicable to real life problems has gradually been proven by researchers in various branches of science. Such works are for instance found in biology [8,11,12,20,21], in economy [9], and in physics [8,10].…”

Section: Introductionmentioning

confidence: 97%

“…Recent research has concentrated on showing the advantages of fractional over classical calculus [4,[8][9][10][11]. In many cases, the fractional calculus has provided better results compared to those obtained via the classical approach.…”

Section: Introductionmentioning

confidence: 99%

On numerical techniques for solving the fractional logistic differential equation

2019

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This paper studied the existence and uniqueness of the solution of the fractional logistic differential equation using Hadamard derivative and integral. Previous work has shown that there is not an exact solution to this fractional model. Hence several numerical approaches, such as generalized Euler's method (GEM), power series expansion (PSE) method, and Caputo-Fabrizio (CF) method, were used to compute the solution. The classical solution obtained from the first order non-linear differential equation was also considered to enable the comparison of error levels.

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Modeling Exponential Growth and Exponential Decay Real Phenomena by Ψ-Caputo Fractional Derivative

Cited by 18 publications

References 0 publications

Existence of Solutions for Anti-Periodic Fractional Differential Inclusions with ψ-Caupto Fractional Derivative

Existence of Solutions for Anti-Periodic Fractional Differential Inclusions with ψ-Caupto Fractional Derivative

Existence of Solutions for Anti-Periodic Fractional Differential Inclusions Involving ψ-Riesz-Caputo Fractional Derivative

On numerical techniques for solving the fractional logistic differential equation

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