Abstract
This paper proposes a new operational numerical method based on Touchard wavelets for solving fractional pantograph differential equations. First, we present an operational matrix of fractional integration as well as the fractional derivative of the Touchard wavelets. Then, by approximating the fractional derivative of the unknown function in terms of the Touchard wavelets and also by using collocation method, the original problem is reduced to a system of algebraic equations. Finally, to show the accuracy and the validity of the proposed technique, we provide some numerical examples.
References
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© 2024 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- New analytical technique to solve fractional-order Sharma–Tasso–Olver differential equation using Caputo and Atangana–Baleanu derivative operators
- Nondensely defined partial neutral functional integrodifferential equations with infinite delay under the light of integrated resolvent operators
- On the number of limit cycles coming from a uniform isochronous center with continuous and discontinuous quartic perturbations
- On ℐ2(𝒮θ p,r )-summability of double sequences in neutrosophic normed spaces
- Earthquake convexity and some new related inequalities
- On λ-statistically φ-convergence
- Multivalued relation-theoretic weak contractions and applications
- Titchmarsh’s theorem with moduli of continuity in Laguerre hypergroup
- Application of Touchard wavelet to simulate numerical solutions to fractional pantograph differential equations
- Existence and linear independence theorem for linear fractional differential equations with constant coefficients
- A study on δ‐ℐ‐compactness in a mixed fuzzy ideal topological space
- Lie symmetry, exact solutions and conservation laws of time fractional Black–Scholes equation derived by the fractional Brownian motion
- On statistical convergence of order α of sequences in gradual normed linear spaces
- Uniqueness of meromorphic functions and their powers in set sharing
- Multiplicative 𝔪-metric space, fixed point theorems with applications in multiplicative integrals equation and numerical results
- Note on bounds on the coefficients of a subclass of m-fold symmetric bi-univalent functions
- Multiple solitons, periodic solutions and other exact solutions of a generalized extended (2 + 1)-dimensional Kadomstev--Petviashvili equation
Articles in the same Issue
- Frontmatter
- New analytical technique to solve fractional-order Sharma–Tasso–Olver differential equation using Caputo and Atangana–Baleanu derivative operators
- Nondensely defined partial neutral functional integrodifferential equations with infinite delay under the light of integrated resolvent operators
- On the number of limit cycles coming from a uniform isochronous center with continuous and discontinuous quartic perturbations
- On ℐ2(𝒮θ p,r )-summability of double sequences in neutrosophic normed spaces
- Earthquake convexity and some new related inequalities
- On λ-statistically φ-convergence
- Multivalued relation-theoretic weak contractions and applications
- Titchmarsh’s theorem with moduli of continuity in Laguerre hypergroup
- Application of Touchard wavelet to simulate numerical solutions to fractional pantograph differential equations
- Existence and linear independence theorem for linear fractional differential equations with constant coefficients
- A study on δ‐ℐ‐compactness in a mixed fuzzy ideal topological space
- Lie symmetry, exact solutions and conservation laws of time fractional Black–Scholes equation derived by the fractional Brownian motion
- On statistical convergence of order α of sequences in gradual normed linear spaces
- Uniqueness of meromorphic functions and their powers in set sharing
- Multiplicative 𝔪-metric space, fixed point theorems with applications in multiplicative integrals equation and numerical results
- Note on bounds on the coefficients of a subclass of m-fold symmetric bi-univalent functions
- Multiple solitons, periodic solutions and other exact solutions of a generalized extended (2 + 1)-dimensional Kadomstev--Petviashvili equation