An efficient operation matrix method for solving fractal–fractional differential equations with generalized Caputo-type fractional–fractal derivative
In this study, we present the new generalized derivative and integral operators which are based on the newly constructed new generalized Caputo fractal–fractional derivatives (NGCFFDs). Based on these operators, a numerical method is developed to solve the fractal–fractional differential equations (...
| Main Authors: | , , , |
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| Format: | Article |
| Published: |
Elsevier
2021
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| Online Access: | http://psasir.upm.edu.my/id/eprint/95827/ |
| _version_ | 1848862230338076672 |
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| author | A.M., Shloof Senu, Norazak Ahmadian, Ali Salahshour, Soheil |
| author_facet | A.M., Shloof Senu, Norazak Ahmadian, Ali Salahshour, Soheil |
| author_sort | A.M., Shloof |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this study, we present the new generalized derivative and integral operators which are based on the newly constructed new generalized Caputo fractal–fractional derivatives (NGCFFDs). Based on these operators, a numerical method is developed to solve the fractal–fractional differential equations (FFDEs). We approximate the solution of the FFDEs as basis vectors of shifted Legendre polynomials (SLPs). We also extend the derivative operational matrix of SLPs to the generalized derivative operational matrix in the sense of NGCFFDs. The efficiency of the developed numerical method is tested by taking various test examples. We also compare the results of our proposed method with the methods existed in the literature In this paper, we specified the fractal–fractional differential operator of new generalized Caputo in three categories: (i) different values in and fractal parameters, (ii) different values in fractional parameter while fractal and parameters are fixed, and (iii) different values in fractal parameter controlling fractional and
parameters. |
| first_indexed | 2025-11-15T13:13:43Z |
| format | Article |
| id | upm-95827 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T13:13:43Z |
| publishDate | 2021 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-958272023-04-04T04:18:37Z http://psasir.upm.edu.my/id/eprint/95827/ An efficient operation matrix method for solving fractal–fractional differential equations with generalized Caputo-type fractional–fractal derivative A.M., Shloof Senu, Norazak Ahmadian, Ali Salahshour, Soheil In this study, we present the new generalized derivative and integral operators which are based on the newly constructed new generalized Caputo fractal–fractional derivatives (NGCFFDs). Based on these operators, a numerical method is developed to solve the fractal–fractional differential equations (FFDEs). We approximate the solution of the FFDEs as basis vectors of shifted Legendre polynomials (SLPs). We also extend the derivative operational matrix of SLPs to the generalized derivative operational matrix in the sense of NGCFFDs. The efficiency of the developed numerical method is tested by taking various test examples. We also compare the results of our proposed method with the methods existed in the literature In this paper, we specified the fractal–fractional differential operator of new generalized Caputo in three categories: (i) different values in and fractal parameters, (ii) different values in fractional parameter while fractal and parameters are fixed, and (iii) different values in fractal parameter controlling fractional and parameters. Elsevier 2021 Article PeerReviewed A.M., Shloof and Senu, Norazak and Ahmadian, Ali and Salahshour, Soheil (2021) An efficient operation matrix method for solving fractal–fractional differential equations with generalized Caputo-type fractional–fractal derivative. Mathematics and Computers in Simulation, 188. 415 - 435. ISSN 0378-4754 https://www.sciencedirect.com/science/article/pii/S0378475421001506?via%3Dihub 10.1016/j.matcom.2021.04.019 |
| spellingShingle | A.M., Shloof Senu, Norazak Ahmadian, Ali Salahshour, Soheil An efficient operation matrix method for solving fractal–fractional differential equations with generalized Caputo-type fractional–fractal derivative |
| title | An efficient operation matrix method for solving fractal–fractional differential equations with generalized Caputo-type fractional–fractal derivative |
| title_full | An efficient operation matrix method for solving fractal–fractional differential equations with generalized Caputo-type fractional–fractal derivative |
| title_fullStr | An efficient operation matrix method for solving fractal–fractional differential equations with generalized Caputo-type fractional–fractal derivative |
| title_full_unstemmed | An efficient operation matrix method for solving fractal–fractional differential equations with generalized Caputo-type fractional–fractal derivative |
| title_short | An efficient operation matrix method for solving fractal–fractional differential equations with generalized Caputo-type fractional–fractal derivative |
| title_sort | efficient operation matrix method for solving fractal–fractional differential equations with generalized caputo-type fractional–fractal derivative |
| url | http://psasir.upm.edu.my/id/eprint/95827/ http://psasir.upm.edu.my/id/eprint/95827/ http://psasir.upm.edu.my/id/eprint/95827/ |