Numerical Solutions Caused by DGJIM and ADM Methods for Multi-Term Fractional BVP Involving the Generalized <i>ψ</i>-RL-Operators
In this research study, we establish some necessary conditions to check the uniqueness-existence of solutions for a general multi-term <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semanti...
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MDPI AG
2021-03-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/4/532 |
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| author | Shahram Rezapour Sina Etemad Brahim Tellab Praveen Agarwal Juan Luis Garcia Guirao |
| author_facet | Shahram Rezapour Sina Etemad Brahim Tellab Praveen Agarwal Juan Luis Garcia Guirao |
| author_sort | Shahram Rezapour |
| collection | DOAJ |
| description | In this research study, we establish some necessary conditions to check the uniqueness-existence of solutions for a general multi-term <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-fractional differential equation via generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-integral boundary conditions with respect to the generalized asymmetric operators. To arrive at such purpose, we utilize a procedure based on the fixed-point theory. We follow our study by suggesting two numerical algorithms called the Dafterdar-Gejji and Jafari method (DGJIM) and the Adomian decomposition method (ADM) techniques in which a series of approximate solutions converge to the exact ones of the given <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-RLFBVP and the equivalent <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-integral equation. To emphasize for the compatibility and the effectiveness of these numerical algorithms, we end this investigation by providing some examples showing the behavior of the exact solution of the existing <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-RLFBVP compared with the approximate ones caused by DGJIM and ADM techniques graphically. |
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| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T12:56:23Z |
| publishDate | 2021-03-01 |
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| series | Symmetry |
| spelling | doaj.art-aeafff8f0924408480ddf56a4c5c7d892023-11-21T11:55:16ZengMDPI AGSymmetry2073-89942021-03-0113453210.3390/sym13040532Numerical Solutions Caused by DGJIM and ADM Methods for Multi-Term Fractional BVP Involving the Generalized <i>ψ</i>-RL-OperatorsShahram Rezapour0Sina Etemad1Brahim Tellab2Praveen Agarwal3Juan Luis Garcia Guirao4Department of Medical Research, China Medical University Hospital, Taichung 404, TaiwanDepartment of Mathematics, Azarbaijan Shahid Madani University, Tabriz 51368, IranLaboratory of Applied Mathematics, Kasdi Merbah University, B.P. 511, Ouargla 30000, AlgeriaDepartment of Mathematics, Anand International College of Engineering, Jaipur 303012, IndiaDepartamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Campus de la Muralla, 30203 Cartagena, Murcia, SpainIn this research study, we establish some necessary conditions to check the uniqueness-existence of solutions for a general multi-term <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-fractional differential equation via generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-integral boundary conditions with respect to the generalized asymmetric operators. To arrive at such purpose, we utilize a procedure based on the fixed-point theory. We follow our study by suggesting two numerical algorithms called the Dafterdar-Gejji and Jafari method (DGJIM) and the Adomian decomposition method (ADM) techniques in which a series of approximate solutions converge to the exact ones of the given <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-RLFBVP and the equivalent <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-integral equation. To emphasize for the compatibility and the effectiveness of these numerical algorithms, we end this investigation by providing some examples showing the behavior of the exact solution of the existing <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-RLFBVP compared with the approximate ones caused by DGJIM and ADM techniques graphically.https://www.mdpi.com/2073-8994/13/4/532ADM numerical methodDGJIM numerical methodboundary value problemexistence |
| spellingShingle | Shahram Rezapour Sina Etemad Brahim Tellab Praveen Agarwal Juan Luis Garcia Guirao Numerical Solutions Caused by DGJIM and ADM Methods for Multi-Term Fractional BVP Involving the Generalized <i>ψ</i>-RL-Operators Symmetry ADM numerical method DGJIM numerical method boundary value problem existence |
| title | Numerical Solutions Caused by DGJIM and ADM Methods for Multi-Term Fractional BVP Involving the Generalized <i>ψ</i>-RL-Operators |
| title_full | Numerical Solutions Caused by DGJIM and ADM Methods for Multi-Term Fractional BVP Involving the Generalized <i>ψ</i>-RL-Operators |
| title_fullStr | Numerical Solutions Caused by DGJIM and ADM Methods for Multi-Term Fractional BVP Involving the Generalized <i>ψ</i>-RL-Operators |
| title_full_unstemmed | Numerical Solutions Caused by DGJIM and ADM Methods for Multi-Term Fractional BVP Involving the Generalized <i>ψ</i>-RL-Operators |
| title_short | Numerical Solutions Caused by DGJIM and ADM Methods for Multi-Term Fractional BVP Involving the Generalized <i>ψ</i>-RL-Operators |
| title_sort | numerical solutions caused by dgjim and adm methods for multi term fractional bvp involving the generalized i ψ i rl operators |
| topic | ADM numerical method DGJIM numerical method boundary value problem existence |
| url | https://www.mdpi.com/2073-8994/13/4/532 |
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