FRACTIONAL POWER SERIES APPROACH FOR THE SOLUTION OF FRACTIONAL-ORDER INTEGRO-DIFFERENTIAL EQUATIONS

Muhammad Akbar (), Rashid Nawaz (), Sumbal Ahsan (), Kottakkaran Sooppy Nisar, Kamal Shah (), Emad E. Mahmoud () and M. M. Alqarni ()
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Muhammad Akbar: Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa, Pakistan
Rashid Nawaz: Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa, Pakistan
Sumbal Ahsan: Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa, Pakistan
Kottakkaran Sooppy Nisar: ��Department of Mathematics, College of Arts and Sciences, Wadi Aldawaser, Prince Sattam bin Abdulaziz University, Saudi Arabia
Kamal Shah: ��Department of mathematics, University of Malakand, Chakdara Dir (L), Khyber Pakhtunkhwa, Pakistan
Emad E. Mahmoud: �Department of Mathematics and Statistics, College of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia
M. M. Alqarni: �Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-8

Abstract: Fractional differential and integral equations are focus of the researchers owing to their tremendous applications in different field of science and technology, such as physics, chemistry, mathematical biology, dynamical system and engineering. In this work, a power series approach called Residual Power Series Method (RPSM) is applied for the solution of fractional (non-integer) order integro-differential equations (FIDEs). The Caputo sense is used for calculating fractional derivatives. Comparison of the obtained solution is made with the Trigonometric Transform Method (TTM) and Optimal Homotopy Asymptotic Method (OHAM). There is no restrictive condition on the proposed solution. The presented technique is simple in applicability and easily computable.

Keywords: RPSM; Caputo Fractional Derivative; Approximate Solution; FIDEs (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22400163

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