Abstract
A new approximate technique is introduced to find a solution of FVFIDE with mixed boundary conditions. This paper started from the meaning of Caputo fractional differential operator. The fractional derivatives are replaced by the Caputo operator, and the solution is demonstrated by the hybrid orthonormal Bernstein and block-pulse functions wavelet method (HOBW). We demonstrate the convergence analysis for this technique to emphasize its reliability. The applicability of the HOBW is demonstrated using three examples. The approximate results of this technique are compared with the correct solutions, which shows that this technique has approval with the correct solutions to the problems.
Highlights
1 Introduction The applications of fractional calculus can be observed in many fields of physics and engineering such as fluid dynamic traffic [1] and signal processing [2]
We demonstrate the following form of FVFIDE that we will solve by the HOBW technique
8 Conclusion In this work, we have fully attempted to find the numerical solution of the fractional system of Volterra integro differential equations by using the HOBW method
Summary
The applications of fractional calculus can be observed in many fields of physics and engineering such as fluid dynamic traffic [1] and signal processing [2]. We derive the approximate solution of FVFIDE using HOBW. Definition 2.2 ([15]) The Riemann fractional integral of order α > 0 of a function f is given by. Where the fractional derivative Dα∗ f (t) is not zero for constant function when α ∈/ N , from when γ. 3.2 Function approximation by the HOBW functions Any function y(t), which is integrable in [0, 1), is truncated by the HOBW method as follows:. Yi(x) of Eq (4.3) is replaced with the approximate solution CiT HOBW(x) as follows: CiT HOBW(xi). From (4.6) give a system of 2k–1M × 2k–1M nonlinear algebraic equations with the same number of unknowns in the vectors C, A, and B Disbanding this system by Newton’s technique, we get the solutions for the unknown vectors C, A, and B. Since ΩL1,L2,K1,K2,α < 1 by contraction mapping theorem, problem (2.5) has a unique solution in C[0, 1]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
