RESEARCH ARTICLE
Modified Galerkin algorithm for solving multitype fractional differential equations
Muhammad M. Alsuyuti,
Eid H. Doha,
Samer S. Ezz-Eldien,
Bayoumi I. Bayoumi,
Dumitru Baleanu,
Muhammad M. Alsuyuti
Department of Basic Science, Egyptian Academy for Engineering and Advanced Technology Affiliated to Ministry of Military Production, Cairo, Egypt
Search for more papers by this authorEid H. Doha
Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt
Search for more papers by this authorCorresponding Author
Samer S. Ezz-Eldien
Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023 China
College of Education, King Saud University, Saudi Arabia
Department of Mathematics, Faculty of Science, New Valley University, Kharga, Egypt
Correspondence
Samer S. Ezz-Eldien, Department of Mathematics, Faculty of Science, New Valley University, Kharga 72511, Egypt.
Email: [email protected]
Communicated by: A. Debbouche
Search for more papers by this authorBayoumi I. Bayoumi
Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, Egypt
Search for more papers by this authorDumitru Baleanu
Department of Mathematics, Cankaya University, 06530 Balgat, Ankara, Turkey
Institute of Space Sciences, Magurele-Bucharest, Romania
Search for more papers by this authorMuhammad M. Alsuyuti,
Eid H. Doha,
Samer S. Ezz-Eldien,
Bayoumi I. Bayoumi,
Dumitru Baleanu,
Muhammad M. Alsuyuti
Department of Basic Science, Egyptian Academy for Engineering and Advanced Technology Affiliated to Ministry of Military Production, Cairo, Egypt
Search for more papers by this authorEid H. Doha
Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt
Search for more papers by this authorCorresponding Author
Samer S. Ezz-Eldien
Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023 China
College of Education, King Saud University, Saudi Arabia
Department of Mathematics, Faculty of Science, New Valley University, Kharga, Egypt
Correspondence
Samer S. Ezz-Eldien, Department of Mathematics, Faculty of Science, New Valley University, Kharga 72511, Egypt.
Email: [email protected]
Communicated by: A. Debbouche
Search for more papers by this authorBayoumi I. Bayoumi
Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, Egypt
Search for more papers by this authorDumitru Baleanu
Department of Mathematics, Cankaya University, 06530 Balgat, Ankara, Turkey
Institute of Space Sciences, Magurele-Bucharest, Romania
Search for more papers by this authorAbstract
The primary point of this manuscript is to dissect and execute a new modified Galerkin algorithm based on the shifted Jacobi polynomials for solving fractional differential equations (FDEs) and system of FDEs (SFDEs) governed by homogeneous and nonhomogeneous initial and boundary conditions. In addition, we apply the new algorithm for solving fractional partial differential equations (FPDEs) with Robin boundary conditions and time-fractional telegraph equation. The key thought for obtaining such algorithm depends on choosing trial functions satisfying the underlying initial and boundary conditions of such problems. Some illustrative examples are discussed to ascertain the validity and efficiency of the proposed algorithm. Also, some comparisons with some other existing spectral methods in the literature are made to highlight the superiority of the new algorithm.
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