Analytical solution of the Atangana–Baleanu–Caputo fractional differential equations using Pythagorean fuzzy sets

M Akram, G Muhammad, D Ahmad - Granular Computing, 2023 - Springer
Every real-world physical phenomena is inherently based on uncertainty and vagueness.
There is a frequent need of a useful tool that can handle the uncertainty, solve and explain …

Higher order approximations for fractional order integro-parabolic partial differential equations on an adaptive mesh with error analysis

S Santra, J Mohapatra, P Das, D Choudhuri - Computers & Mathematics …, 2023 - Elsevier
This work deals with a higher order numerical approximation for analyzing a class of multi-
term time fractional partial integro-differential equations involving Volterra integral operators …

Fuzzy conformable fractional differential equations: novel extended approach and new numerical solutions

OA Arqub, M Al-Smadi - Soft Computing, 2020 - Springer
The aim of this article is to propose a new definition of fuzzy fractional derivative, so-called
fuzzy conformable. To this end, we discussed fuzzy conformable fractional integral softly …

Application of residual power series method for the solution of time-fractional Schrödinger equations in one-dimensional space

O Abu Arqub - Fundamenta Informaticae, 2019 - journals.sagepub.com
The object of this article is to present the computational solution of the time-fractional
Schrödinger equation subject to given constraint condition based on the generalized Taylor …

Reproducing kernel approach for numerical solutions of fuzzy fractional initial value problems under the Mittag–Leffler kernel differential operator

O Abu Arqub, J Singh, B Maayah… - … Methods in the Applied …, 2023 - Wiley Online Library
In this research study, fuzzy fractional differential equations in presence of the Atangana–
Baleanu–Caputo differential operators are analytically and numerically treated using …

The Tikhonov regularization method for the inverse source problem of time fractional heat equation in the view of ABC-fractional technique

S Djennadi, N Shawagfeh, MS Osman… - Physica …, 2021 - iopscience.iop.org
This research considers an inverse source problem for fractional diffusion equation that
containing fractional derivative with non-singular and non-local kernel, namely, Atangana …

Adaptation of kernel functions‐based approach with Atangana–Baleanu–Caputo distributed order derivative for solutions of fuzzy fractional Volterra and Fredholm …

O Abu Arqub, J Singh… - Mathematical Methods in …, 2023 - Wiley Online Library
Mathematical modeling of uncertain fractional integrodifferentials (FIDEs) is an extremely
significant topic in electric circuits, signal processing, electromagnetics, and anomalous …

A fractional Tikhonov regularization method for an inverse backward and source problems in the time-space fractional diffusion equations

S Djennadi, N Shawagfeh, OA Arqub - Chaos, Solitons & Fractals, 2021 - Elsevier
In this research, we deal with two types of inverse problems for diffusion equations involving
Caputo fractional derivatives in time and fractional Sturm-Liouville operator for space. The …

Fuzzy fractional differential equations under the Mittag-Leffler kernel differential operator of the ABC approach: Theorems and applications

M Al-Smadi, OA Arqub, D Zeidan - Chaos, Solitons & Fractals, 2021 - Elsevier
In this manuscript, we introduced, analyzed, and studied fuzzy fractional differential
equations in terms of Atangana-Baleanu-Caputo differential operator equipped with …

Numerical computations of coupled fractional resonant Schrödinger equations arising in quantum mechanics under conformable fractional derivative sense

M Al-Smadi, OA Arqub, S Momani - Physica Scripta, 2020 - iopscience.iop.org
Mathematical modeling of fractional resonant Schrödinger equations is an extremely
significant topic in the classical of quantum mechanics, chromodynamics, astronomy, and …