On the solvability fractional of a boundary value problem with new fractional integral

In this article, we investigate the existence and uniqueness of the solution of a fractional boundary value problem with conformable fractional derivation of the Caputo-Fabrizio type. In order to study this problem we used a new definition of fractional integral as an inverse of the conformable fractional derivative of Caputo-Fabrizio, therefore, so we transformed the problem to a equivalent linear Volterra-Fredholm integral equations of the second kind, and taking sufficient conditions existence and uniqueness of this solution is proven based on the results obtained. The analytical study is followed by a complete numerical study.

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Numerical solution of fractional boundary value problem with caputo-fabrizio and its fractional integral

Bekkouche

Mansouri

Ahmed

2022

J. Appl. Math. Comput.

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Stability of the mixed Caputo fractional integro-differential equation by means of weighted space method

Dai¹,

Liu

2022

MATH

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<abstract><p>In this research work, we consider a class of nonlinear fractional integro-differential equations containing Caputo fractional derivative and integral derivative. We discuss the stabilities of Ulam-Hyers, Ulam-Hyers-Rassias, semi-Ulam-Hyers-Rassias for the nonlinear fractional integro-differential equations in terms of weighted space method and Banach fixed-point theorem. After the demonstration of our results, an example is given to illustrate the results we obtained.</p></abstract>

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Orthonormal Euler wavelets method for time-fractional Cattaneo equation with Caputo-Fabrizio derivative

Xu¹,

Zhou

2023

MATH

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<abstract><p>In this paper, a new orthonormal wavelets based on the orthonormal Euler polynomials (OEPs) is constructed to approximate the numerical solution of time-fractional Cattaneo equation with Caputo-Fabrizio derivative. By applying the Gram-Schmidt orthonormalization process on sets of Euler polynomials of various degrees, an explicit representation of OEPs is obtained. The convergence analysis and error estimate of the orthonormal Euler wavelets expansion are studied. The exact formula of Caputo-Fabrizio fractional integral of orthonormal Euler wavelets are derived using Laplace transform. The applicability and validity of the proposed method are verified by some numerical examples.</p></abstract>

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On the solvability fractional of a boundary value problem with new fractional integral

Cited by 3 publications

References 11 publications

Numerical solution of fractional boundary value problem with caputo-fabrizio and its fractional integral

Numerical solution of fractional boundary value problem with caputo-fabrizio and its fractional integral

Stability of the mixed Caputo fractional integro-differential equation by means of weighted space method

Orthonormal Euler wavelets method for time-fractional Cattaneo equation with Caputo-Fabrizio derivative

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