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A highly accurate Hermite polynomial-based least-squares approach for solving fractional Volterra-Fredholm integro-differential equations.

• Authors : Hamood MM; Department of Mathematics, Taiz University, Taiz, Yemen.; Department of Mathematics, Hodeidah University, AL-Hudaydah, Yemen.

Subjects: Algorithms* ; Models, Theoretical*; Least-Squares Analysis

• Source: PloS one [PLoS One] 2026 Apr 07; Vol. 21 (4), pp. e0346080. Date of Electronic Publication: 2026 Apr 07 (Print Publication: 2026).Publisher: Public Library of Science Country of Publication: United States NLM ID: 101285081 Publication Model: eCollection Cited Medium: Internet

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Solving 2nd Order Volterra Integro-Differential Equations by Using IDRLnet Library and Physics-informed neural networks.

• Authors : Jasim, Oday Ahmed¹ ; Al-Rozbayani, Abdulghafor M.²

Subjects: *Volterra equations; *Partial differential equations; *Numerical analysis

• Source: Iraqi Journal of Science. 2026, Vol. 67 Issue 3, p1668-1684. 17p.

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Algorithms for Solving Ordinary Differential Equations Based on Orthogonal Polynomial Neural Networks.

• Authors : Parovik, Roman¹ (AUTHOR)

• Source: Algorithms. Jan2026, Vol. 19 Issue 1, p82. 15p.

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Asymptotic expansions as control variates for deep solvers to fully-coupled forward-backward stochastic differential equations.

• Authors : Naito M; Tokyo Metropolitan University, Graduate School of Management, Tokyo, Japan.; Saito T

Subjects: Algorithms* ; Neural Networks, Computer*; Stochastic Processes

• Source: PloS one [PLoS One] 2025 May 28; Vol. 20 (5), pp. e0321778. Date of Electronic Publication: 2025 May 28 (Print Publication: 2025).Publisher: Public Library of Science Country of Publication: United States NLM ID: 101285081 Publication Model: eCollection Cited Medium: Internet

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Duality of Shehu transform with other well known transforms and application to fractional order differential equations.

• Authors : Mlaiki N; Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia.; Jamal N

Subjects: Algorithms* ; Models, Theoretical* ; Mathematics*

• Source: PloS one [PLoS One] 2025 Apr 29; Vol. 20 (4), pp. e0318157. Date of Electronic Publication: 2025 Apr 29 (Print Publication: 2025).Publisher: Public Library of Science Country of Publication: United States NLM ID: 101285081 Publication Model: eCollection Cited Medium: Internet

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Residual-Based Improved Uncertain Maximum Likelihood Estimation for Uncertain Delay Differential Equations.

• Authors : Wang, Han¹ (AUTHOR); Zhang, Zhiqiang¹ (AUTHOR); Shi, Haiyan¹ (AUTHOR)

• Source: Symmetry (20738994). Nov2025, Vol. 17 Issue 11, p1939. 20p.

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Spectral Collocation Method for Solving Nonlinear Riesz Distributed-Order Fractional Differential Equations.

• Authors : Lachin, Ammar¹ (AUTHOR); Abdelkawy, Mohammed A.² (AUTHOR); Sathasivam, Saratha¹ (AUTHOR)

• Source: Mathematics (2227-7390). Nov2025, Vol. 13 Issue 21, p3425. 24p.

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Two Numerical Approaches to Solving Fractional Differential Equations with a Generalized Mittag–Leffler Kernel Using Bernstein Polynomials.

• Authors : Tamimi, Shreen¹ ; Alomari, A. K.² ; Alaroud, M.¹

• Source: European Journal of Pure & Applied Mathematics. Oct2025, Vol. 18 Issue 4, p1-19. 19p.

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Numerical Computations of Fractional Differential Equations in Engineering using the Polynomial Least Squares Method.

• Authors : Ahmed, Shakeel¹ ; Ullah, Saif² ; Rasool, Faiza tul¹

• Source: Journal of Prime Research in Mathematics. 2025, Vol. 21 Issue 2, p13-24. 12p.

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A novel technique using integral transforms and residual functions for nonlinear partial fractional differential equations involving Caputo derivatives.

• Authors : Khan ZA; Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.; Riaz MB

Subjects: Nonlinear Dynamics* ; Algorithms*; Models, Theoretical

• Source: PloS one [PLoS One] 2024 Dec 19; Vol. 19 (12), pp. e0313860. Date of Electronic Publication: 2024 Dec 19 (Print Publication: 2024).Publisher: Public Library of Science Country of Publication: United States NLM ID: 101285081 Publication Model: eCollection Cited Medium: Internet

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