Applications of fractional power series approach in solving fractional Volterra integro-differential equations

Saleh Alshammari; Mohammed Al-Smadi; Ishak Hashim; Mohd Almie Alias

doi:10.1063/1.5111210

Applications of fractional power series approach in solving fractional Volterra integro-differential equations

Saleh Alshammari
, Mohammed Al-Smadi
, Ishak Hashim
, Mohd Almie Alias

Universiti Kebangsaan Malaysia
Al-Balqa Applied University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

10 Scopus citations

Abstract

This paper is focused at constructing an analytic-numeric solution based on fractional power series expansion for the fractional integro-differential equations of Volterra type by using residual power series approach. This RPS method gives approximate solutions in convergent series formula with surely computable components. Illustrative numerical example is included to demonstrate efficiency, accuracy, and applicability of the RPS method. Numerical results obtained indicate that the exact solution in good agreement with approximate solutions.

Original language	English
Title of host publication	2018 UKM FST Postgraduate Colloquium
Subtitle of host publication	Proceedings of the Universiti Kebangsaan Malaysia, Faculty of Science and Technology 2018 Postgraduate Colloquium
Editors	Noor Hayati Ahmad Rasol, Kamarulzaman Ibrahim, Siti Aishah Hasbullah, Mohammad Hafizuddin Hj. Jumali, Nazlina Ibrahim, Marlia Mohd Hanafiah, Mohd Talib Latif
Publisher	American Institute of Physics Inc.
ISBN (Electronic)	9780735418431
DOIs	https://doi.org/10.1063/1.5111210
State	Published - 27 Jun 2019
Externally published	Yes
Event	2018 UKM FST Postgraduate Colloquium - Selangor, Malaysia Duration: 4 Apr 2018 → 6 Apr 2018

Publication series

Name	AIP Conference Proceedings
Volume	2111
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	2018 UKM FST Postgraduate Colloquium
Country/Territory	Malaysia
City	Selangor
Period	4/04/18 → 6/04/18

Access to Document

10.1063/1.5111210

Cite this

Alshammari, S., Al-Smadi, M., Hashim, I., & Alias, M. A. (2019). Applications of fractional power series approach in solving fractional Volterra integro-differential equations. In N. H. A. Rasol, K. Ibrahim, S. A. Hasbullah, M. H. H. Jumali, N. Ibrahim, M. M. Hanafiah, & M. T. Latif (Eds.), 2018 UKM FST Postgraduate Colloquium: Proceedings of the Universiti Kebangsaan Malaysia, Faculty of Science and Technology 2018 Postgraduate Colloquium Article 020003 (AIP Conference Proceedings; Vol. 2111). American Institute of Physics Inc.. https://doi.org/10.1063/1.5111210

Alshammari, Saleh ; Al-Smadi, Mohammed ; Hashim, Ishak et al. / Applications of fractional power series approach in solving fractional Volterra integro-differential equations. 2018 UKM FST Postgraduate Colloquium: Proceedings of the Universiti Kebangsaan Malaysia, Faculty of Science and Technology 2018 Postgraduate Colloquium. editor / Noor Hayati Ahmad Rasol ; Kamarulzaman Ibrahim ; Siti Aishah Hasbullah ; Mohammad Hafizuddin Hj. Jumali ; Nazlina Ibrahim ; Marlia Mohd Hanafiah ; Mohd Talib Latif. American Institute of Physics Inc., 2019. (AIP Conference Proceedings).

@inproceedings{eed4b150ccbc4fe2811405f5cce4e66a,

title = "Applications of fractional power series approach in solving fractional Volterra integro-differential equations",

abstract = "This paper is focused at constructing an analytic-numeric solution based on fractional power series expansion for the fractional integro-differential equations of Volterra type by using residual power series approach. This RPS method gives approximate solutions in convergent series formula with surely computable components. Illustrative numerical example is included to demonstrate efficiency, accuracy, and applicability of the RPS method. Numerical results obtained indicate that the exact solution in good agreement with approximate solutions.",

author = "Saleh Alshammari and Mohammed Al-Smadi and Ishak Hashim and Alias, \{Mohd Almie\}",

note = "Publisher Copyright: {\textcopyright} 2019 Author(s).; 2018 UKM FST Postgraduate Colloquium ; Conference date: 04-04-2018 Through 06-04-2018",

year = "2019",

month = jun,

day = "27",

doi = "10.1063/1.5111210",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics Inc.",

editor = "Rasol, \{Noor Hayati Ahmad\} and Kamarulzaman Ibrahim and Hasbullah, \{Siti Aishah\} and Jumali, \{Mohammad Hafizuddin Hj.\} and Nazlina Ibrahim and Hanafiah, \{Marlia Mohd\} and Latif, \{Mohd Talib\}",

booktitle = "2018 UKM FST Postgraduate Colloquium",

}

Alshammari, S, Al-Smadi, M, Hashim, I & Alias, MA 2019, Applications of fractional power series approach in solving fractional Volterra integro-differential equations. in NHA Rasol, K Ibrahim, SA Hasbullah, MHH Jumali, N Ibrahim, MM Hanafiah & MT Latif (eds), 2018 UKM FST Postgraduate Colloquium: Proceedings of the Universiti Kebangsaan Malaysia, Faculty of Science and Technology 2018 Postgraduate Colloquium., 020003, AIP Conference Proceedings, vol. 2111, American Institute of Physics Inc., 2018 UKM FST Postgraduate Colloquium, Selangor, Malaysia, 4/04/18. https://doi.org/10.1063/1.5111210

Applications of fractional power series approach in solving fractional Volterra integro-differential equations. / Alshammari, Saleh; Al-Smadi, Mohammed; Hashim, Ishak et al.
2018 UKM FST Postgraduate Colloquium: Proceedings of the Universiti Kebangsaan Malaysia, Faculty of Science and Technology 2018 Postgraduate Colloquium. ed. / Noor Hayati Ahmad Rasol; Kamarulzaman Ibrahim; Siti Aishah Hasbullah; Mohammad Hafizuddin Hj. Jumali; Nazlina Ibrahim; Marlia Mohd Hanafiah; Mohd Talib Latif. American Institute of Physics Inc., 2019. 020003 (AIP Conference Proceedings; Vol. 2111).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Applications of fractional power series approach in solving fractional Volterra integro-differential equations

AU - Alshammari, Saleh

AU - Al-Smadi, Mohammed

AU - Hashim, Ishak

AU - Alias, Mohd Almie

PY - 2019/6/27

Y1 - 2019/6/27

N2 - This paper is focused at constructing an analytic-numeric solution based on fractional power series expansion for the fractional integro-differential equations of Volterra type by using residual power series approach. This RPS method gives approximate solutions in convergent series formula with surely computable components. Illustrative numerical example is included to demonstrate efficiency, accuracy, and applicability of the RPS method. Numerical results obtained indicate that the exact solution in good agreement with approximate solutions.

AB - This paper is focused at constructing an analytic-numeric solution based on fractional power series expansion for the fractional integro-differential equations of Volterra type by using residual power series approach. This RPS method gives approximate solutions in convergent series formula with surely computable components. Illustrative numerical example is included to demonstrate efficiency, accuracy, and applicability of the RPS method. Numerical results obtained indicate that the exact solution in good agreement with approximate solutions.

UR - https://www.scopus.com/pages/publications/85068464772

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DO - 10.1063/1.5111210

M3 - Conference contribution

AN - SCOPUS:85068464772

T3 - AIP Conference Proceedings

BT - 2018 UKM FST Postgraduate Colloquium

A2 - Rasol, Noor Hayati Ahmad

A2 - Ibrahim, Kamarulzaman

A2 - Hasbullah, Siti Aishah

A2 - Jumali, Mohammad Hafizuddin Hj.

A2 - Ibrahim, Nazlina

A2 - Hanafiah, Marlia Mohd

A2 - Latif, Mohd Talib

PB - American Institute of Physics Inc.

T2 - 2018 UKM FST Postgraduate Colloquium

Y2 - 4 April 2018 through 6 April 2018

ER -

Alshammari S, Al-Smadi M, Hashim I, Alias MA. Applications of fractional power series approach in solving fractional Volterra integro-differential equations. In Rasol NHA, Ibrahim K, Hasbullah SA, Jumali MHH, Ibrahim N, Hanafiah MM, Latif MT, editors, 2018 UKM FST Postgraduate Colloquium: Proceedings of the Universiti Kebangsaan Malaysia, Faculty of Science and Technology 2018 Postgraduate Colloquium. American Institute of Physics Inc. 2019. 020003. (AIP Conference Proceedings). doi: 10.1063/1.5111210

Applications of fractional power series approach in solving fractional Volterra integro-differential equations

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