Upper-solution or lower-solution method for Langevin equations with n fractional orders

Beddani, Hamid

doi:10.2298/fil2114743h

Filomat

2021

DOI: 10.2298/fil2114743h

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Upper-solution or lower-solution method for Langevin equations with n fractional orders

Hamid Beddani

Abstract: In this paper, we study a nonlinear Langevin equation involving n-parameter singular fractional orders ?i(i=1,2), and ? with initial conditions. By means of an interesting fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions for the fractional equations.

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Cited by 2 publications

References 16 publications

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An analytical approach for the fractional-order Hepatitis B model using new operator

Ghosh

2023

Int. J. Biomath.

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In this work, the main goal is to implement Homotopy perturbation transform method (HPTM) involving Katugampola fractional operator. As an example, a fractional order Hepatitis model is considered to analyze the solutions. At first, the integer order model is converted to fractional order model in Caputo sense. Then, the new operator Katugampola fractional derivative is used to present the model. The new such kind of operator is illustrated in Caputo sense. HPTM is described to get the solution of the proposed model using the new kind of operator. Also, there are some analyses about the new kind of operator to prove the efficiency of the operator.

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An analytical approach for the fractional-order Hepatitis B model using new operator

Ghosh

2023

Int. J. Biomath.

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Positive solutions for a class of nonlinear p-Laplacian Hadamard fractional differential systems with coupled nonlocal Riemann-Stieltjes integral boundary conditions

Yang

2022

Filomat

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This paper investigates a class of nonlinear p-Laplacian Hadamard fractional differential systems with coupled nonlocal Riemann-Stieltjes integral boundary conditions. First, we obtain the corresponding Green?s function for the considered boundary value problems and some of its properties. Then, by using the Guo-Krasnosel?skii fixed point theorem, some sufficient conditions for existence and nonexistence of positive solutions for the addressed systems are obtained under the different intervals of the parameters ? and ?. As applications, some examples are presented to show the effectiveness of the main results.

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Upper-solution or lower-solution method for Langevin equations with n fractional orders

Cited by 2 publications

References 16 publications

An analytical approach for the fractional-order Hepatitis B model using new operator

An analytical approach for the fractional-order Hepatitis B model using new operator

Positive solutions for a class of nonlinear p-Laplacian Hadamard fractional differential systems with coupled nonlocal Riemann-Stieltjes integral boundary conditions

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