Search Results - "fractional initial value problem"

Solution of Nonhomogeneous Linear System of Caputo Fractional Differential Equations with Initial Conditions

Authors: Aghalaya S. Vatsala Govinda Pageni

Source: Axioms, Vol 14, Iss 10, p 736 (2025)

Subject Terms: caputo fractional derivative, fractional initial value problem, matrix Mittag–Leffler function, Mathematics, QA1-939

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Relation: https://www.mdpi.com/2075-1680/14/10/736; https://doaj.org/toc/2075-1680

Access URL: https://doaj.org/article/f433913ce132466ebeb3509a575aaba2

Trapezoidal Scheme for the Numerical Solution of Fractional Initial Value Problems

Authors: Batiha, Iqbal M. Alsamad, Hebah F. Jebril, Iqbal H. et al.

Source: International Journal of Robotics and Control Systems; Vol 5, No 2 (2025); 1238-1253 ; 2775-2658

Subject Terms: Fractional Calculus, Fractional Initial Value Problem, Fractional Taylor Formula, Fractional Trapezoid Method

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Relation: https://pubs2.ascee.org/index.php/IJRCS/article/view/1795/pdf; https://pubs2.ascee.org/index.php/IJRCS/article/view/1795

Availability: https://pubs2.ascee.org/index.php/IJRCS/article/view/1795
https://doi.org/10.31763/ijrcs.v5i2.1795

Approximation of Fractional Caputo Derivative of Variable Order and Variable Terminals with Application to Initial/Boundary Value Problems

Authors: Paulina Stempin Wojciech Sumelka

Source: Fractal and Fractional ; Volume 9 ; Issue 5 ; Pages: 269

Subject Terms: fractional calculus, fractional differential equation, fractional boundary value problem, fractional initial value problem, fractional derivative approximation, fractional variable order, variable terminal of fractional derivative

File Description: application/pdf

Relation: General Mathematics, Analysis; https://dx.doi.org/10.3390/fractalfract9050269

Availability: https://doi.org/10.3390/fractalfract9050269

Fractional Laplace transform for matrix valued functions with applications

Authors: Ahmed Bouchenak Mohammed Al Horani Jihad Younis et al.

Source: Arab Journal of Basic and Applied Sciences, Vol 29, Iss 1, Pp 330-336 (2022)

Subject Terms: Composite material, Vector-valued functions, Fractional Differential Equations, Laplace transform, Science, Matrix (chemical analysis), conformable derivative, matrix-valued functions, 34A08, Laplace–Stieltjes transform, Mathematical analysis, 01 natural sciences, Orthogonal Polynomials, Convergence Analysis of Iterative Methods for Nonlinear Equations, Fractional Integrals, Green's function for the three-variable Laplace equation, 0103 physical sciences, FOS: Mathematics, 0101 mathematics, Anomalous Diffusion Modeling and Analysis, Two-sided Laplace transform, Numerical Analysis, Applied Mathematics, 4. Education, Post's inversion formula, Applied mathematics, Computer science, Materials science, Fourier analysis, Fractional Fourier transform, Fractional Derivatives, Modeling and Simulation, Physical Sciences, Fourier transform, Fractional Calculus, fractional initial value problem, Mathematics, fractional Laplace transform, Inverse Laplace transform

Access URL: https://doaj.org/article/5f8f9cbf849e4b2facdabb3f5ffe518b

Remarks on Sequential Caputo Fractional Differential Equations with Fractional Initial and Boundary Conditions

Authors: Aghalaya S. Vatsala Bhuvaneswari Sambandham

Source: Mathematics, Vol 12, Iss 24, p 3970 (2024)

Subject Terms: sequential Caputo fractional derivative, fractional initial value problem, fractional boundary value problem, Mittag–Leffler function, Mathematics, QA1-939

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Relation: https://www.mdpi.com/2227-7390/12/24/3970; https://doaj.org/toc/2227-7390

Access URL: https://doaj.org/article/8014bfa3c6ed468696d06a1bce8c2604

New generalizations for Gronwall type inequalities involving a $ \psi $-fractional operator and their applications

Authors: Jehad Alzabut Yassine Adjabi Weerawat Sudsutad et al.

Source: AIMS Mathematics, Vol 6, Iss 5, Pp 5053-5077 (2021)

Subject Terms: Operator (biology), Theory and Applications of Fractional Differential Equations, Mathematical analysis, Biochemistry, Gene, 01 natural sciences, Machine learning, QA1-939, FOS: Mathematics, 0101 mathematics, Stability (learning theory), ψ-fractional operators, Biology, Anomalous Diffusion Modeling and Analysis, generalized gronwall's inequality, Ecology, ulam-hyers stability, Applied Mathematics, Applied mathematics, Computer science, Nonlocal Partial Differential Equations and Boundary Value Problems, Gronwall's inequality, Fractional Derivatives, Chemistry, Inequality, Modeling and Simulation, FOS: Biological sciences, Physical Sciences, Repressor, Uniqueness, Transcription factor, ψ-fractional initial value problem, Type (biology), Mathematics, existence and uniqueness

Access URL: https://doaj.org/article/6d99dc14f11b4e45b0d68d8d5058c1c6
https://www.aimspress.com/article/doi/10.3934/math.2021299?viewType=HTML

Approximation of fractional Caputo derivative of variable order and variable terminals with application to initial/boundary-value problems

Authors: Stempin, Paulina orcid:0000-0002-1115- Sumelka, Wojciech

Subject Terms: fractional calculus, fractional differential equation, fractional boundary value problem, fractional initial value problem, fractional derivative approximation, fractional variable order, variable terminal of fractional derivative

Relation: https://zenodo.org/records/14288990; oai:zenodo.org:14288990; https://doi.org/10.5281/zenodo.14288990

Availability: https://doi.org/10.5281/zenodo.14288990
https://zenodo.org/records/14288990

New generalizations for Gronwall type inequalities involving a ψ-fractional operator and their applications

Authors: Jehad Alzabut Yassine Adjabi Weerawat Sudsutad et al.

Source: AIMS Mathematics, Vol 6, Iss 5, Pp 5053-5077 (2021)

Subject Terms: ψ-fractional operators, generalized gronwall's inequality, ψ-fractional initial value problem, existence and uniqueness, ulam-hyers stability, Mathematics, QA1-939

File Description: electronic resource

Relation: https://doaj.org/toc/2473-6988

Access URL: https://doaj.org/article/6d99dc14f11b4e45b0d68d8d5058c1c6

A multiple-step adaptive pseudospectral method for solving multi-order fractional differential equations

Authors: Mohammad Maleki Mahmoud Mashali-Firouzi

Source: Nonlinear Engineering, Vol 8, Iss 1, Pp 702-718 (2019)

Subject Terms: collocation, multiple-step pseudospectral method, shifted legendre-gauss points, error estimates, fractional initial value problem, caputo derivative, TA1-2040, 0101 mathematics, Engineering (General). Civil engineering (General), 01 natural sciences, 6. Clean water

Access URL: https://doaj.org/article/b5f54f15aa234912b6fc2bd4e8284619
https://ui.adsabs.harvard.edu/abs/2019NLE.....8..702M/abstract
https://www.degruyter.com/document/doi/10.1515/nleng-2018-0079/html

Inequalities

Authors: Furuichi, Shigeru

Subject Terms: convex functions, trigonometric inequalities, weaving frame, one-sided weighted Campanato space, frame, higher order convexity, Hadamard fractional integrals, exponential inequalities, Montgomery identity, Steffensen's inequality, quasi-convex, Q1-390, Fejér's inequality, Power mean inequality, half-discrete Hardy-Hilbert's inequality, Katugampola fractional integrals, starlike functions, Hilbert C*-module, Hilbert space, geometrically convex function, Euler-Maclaurin summation formula, quantum estimates, proportional fractional derivative, weaving K-frame, analytic functions, parameter, strongly ?-convex functions, positive linear map, special means, Hermite–Hadamard type inequality, operator Kantorovich inequality, Hermite-Hadamard type inequalities, majorization inequality, Hölder's inequality, bic Book Industry Communication::P Mathematics & science, g-frame, Fink's identity, QA1-939, Riemann–Liouville fractional integrals, ?-variation, reverse inequality, interval-valued functions, Taylor theorem, Green functions, Fekete-Szegö inequality, twice differentiable convex functions, Riemann–Liouville and Caputo proportional fractional initial value problem, weight function, commutator, h2)-convex, refined inequality, (h1, operator inequality, alternate dual frame, Gronwall–Bellman inequality, Hermite-Hadamard inequality, g-Bessel sequence, one-sided singular integral, adjointable operator, power inequalities, K-dual, weaving frame operator, one-sided weighted Morrey space, pseudo-inverse

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Access URL: https://www.mdpi.com/books/pdfview/book/1955
https://directory.doabooks.org/handle/20.500.12854/50175

On the linear fuzzy model associated with Caputo–Fabrizio operator

Authors: R. Abdollahi A. Khastan J. J. Nieto et al.

Source: Boundary Value Problems, Vol 2018, Iss 1, Pp 1-18 (2018)

Subject Terms: Caputo–Fabrizio operator, Fuzzy fractional initial value problem, Generalized differentiability, Fuzzy differential equations, Analysis, QA299.6-433

File Description: electronic resource

Relation: http://link.springer.com/article/10.1186/s13661-018-1010-2; https://doaj.org/toc/1687-2770

Access URL: https://doaj.org/article/7692f6f77f484f49bc71de729d158452

A New Gronwall–Bellman Inequality in Frame of Generalized Proportional Fractional Derivative

Authors: Jehad Alzabut Weerawat Sudsutad Zeynep Kayar et al.

Source: Mathematics, Vol 7, Iss 8, p 747 (2019)

Subject Terms: Gronwall–Bellman inequality, proportional fractional derivative, Riemann–Liouville and Caputo proportional fractional initial value problem, Mathematics, QA1-939

Relation: https://www.mdpi.com/2227-7390/7/8/747; https://doaj.org/toc/2227-7390; https://doaj.org/article/40482a7ea739458fbb322170a6b526dc

Availability: https://doi.org/10.3390/math7080747
https://doaj.org/article/40482a7ea739458fbb322170a6b526dc

A new method for approximating fractional derivatives/ integrals as a series of higher-integer-order derivatives - examples and results of applying the method to initial/boundary value problems ; Nowa metoda aproksymacji pochodnych/całek niecałkowitego rzędu jako szereg pochodnych wyższych całkowitych rzędów - przykłady i wyniki zastosowania metody w problemach wartości początkowej/brzegowej

Authors: Stempin, Paulina orcid:0000-0002-1115-

Subject Terms: fractional derivative, fractional integral, fractional calculus, fractional differential equation, fractional boundary value problem, fractional initial value problem

Relation: https://zenodo.org/records/13344091; oai:zenodo.org:13344091; https://doi.org/10.5281/zenodo.13344091

Availability: https://doi.org/10.5281/zenodo.13344091
https://zenodo.org/records/13344091

Monotone iterative method for fractional differential equations

Authors: Zhanbing Bai Zhang Shuo Sujing Sun et al.

Source: Electronic Journal of Differential Equations, Vol 2016, Iss 06,, Pp 1-8 (2016)

Subject Terms: Fractional initial value problem, lower and upper solution method, existence of solutions, Mathematics, QA1-939

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Relation: http://ejde.math.txstate.edu/Volumes/2016/06/abstr.html; https://doaj.org/toc/1072-6691

Access URL: https://doaj.org/article/29c0e9b6393a46b5bd9dba4347574963

Existence and uniqueness of solution for a nonhomogeneous discrete fractional initial value problem

Authors: Khastan, A. Azadi, H.

Source: Rocky Mountain J. Math. 49, no. 4 (2019), 1237-1257

Subject Terms: discrete Mittag-Leffler function, 39A12, discrete Laplace transform, fractional initial value problem, 0101 mathematics, 26A33, 01 natural sciences, Discrete fractional calculus, 34A25

File Description: application/pdf

Access URL: https://projecteuclid.org/euclid.rmjm/1567044038

A hybrid collocation method for fractional initial value problems

Authors: Wang, Linjun Wang, Fang Cao, Yanzhao

Source: J. Integral Equations Applications 31, no. 1 (2019), 105-129

Subject Terms: Fractional initial value problem, hybrid collocation method, convergence order, 45G10, 65L05, 0101 mathematics, 26A33, weakly singular kernel, 01 natural sciences

File Description: application/pdf

Access URL: https://projecteuclid.org/euclid.jiea/1561601028

Sum and Difference Compositions in Discrete Fractional Calculus

Authors: Holm, Michael

Source: Cubo, Vol 13, Iss 3, Pp 153-184 (2011)
Cubo (Temuco), Volume: 13, Issue: 3, Pages: 153-184, Published: OCT 2011

Subject Terms: Discrete Fractional Calculus, Fractional Sum, Composition Rule, Fractional Difference, Fractional Initial Value Problem, QA1-939, 0101 mathematics, 01 natural sciences, Mathematics

File Description: text/html

Access URL: https://scielo.conicyt.cl/pdf/cubo/v13n3/art09.pdf
https://doaj.org/article/c4e8438d603f48b3be2ecab836ee78f7
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462011000300009
https://scielo.conicyt.cl/pdf/cubo/v13n3/art09.pdf
http://revistas.ufro.cl/ojs/index.php/cubo/article/view/1367
https://www.scielo.cl/pdf/cubo/v13n3/art09.pdf
https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0719-06462011000300009
http://revistas.ufro.cl/ojs/index.php/cubo/article/download/1367/1221
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462011000300009&lng=en&tlng=en

The Laplace transform in discrete fractional calculus

Authors: Michael Holm

Source: Computers & Mathematics with Applications. 62:1591-1601

Subject Terms: Computational Mathematics, Fractional initial value problem, Taylor monomial, Computational Theory and Mathematics, Laplace transform, Modelling and Simulation, 0103 physical sciences, Exponential order, 0101 mathematics, 01 natural sciences, Discrete fractional calculus, Convolution

Access URL: https://dblp.uni-trier.de/db/journals/cma/cma62.html#Holm11
https://www.sciencedirect.com/science/article/pii/S0898122111003208
https://www.sciencedirect.com/science/article/abs/pii/S0898122111003208
https://doi.org/10.1016/j.camwa.2011.04.019
https://dl.acm.org/doi/10.1016/j.camwa.2011.04.019
https://core.ac.uk/display/82230938

Sum and Difference Compositions in Discrete Fractional Calculus

Authors: Michael Holm

Source: Cubo, Vol 13, Iss 3, Pp 153-184 (2011)

Subject Terms: Discrete Fractional Calculus, Fractional Sum, Fractional Difference, Composition Rule, Fractional Initial Value Problem., Mathematics, QA1-939

File Description: electronic resource

Relation: http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462011000300009; https://doaj.org/toc/0716-7776; https://doaj.org/toc/0719-0646

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Monotone iterative method for fractional differential equations

Authors: Bai, Zhanbing Zhang, Shuo Sun, Sujing et al.

Source: Electronic Journal of Differential Equations, 2016, San Marcos, Texas: Texas State University and University of North Texas.

Subject Terms: fractional initial value problem, lower and upper solution method, existence of solutions

File Description: Text; 8 pages; 1 file (.pdf); application/pdf

Relation: https://hdl.handle.net/10877/16878

Availability: https://hdl.handle.net/10877/16878