A numerical method for solving a class of systems of nonlinear Pantograph differential equations
Tài liệu tham khảo
Ravichandran, 2019, New results on existence in the framework of Atangana-Baleanu derivative for fractional integro-differential equations, Chaos Solitons Fract., 125, 194, 10.1016/j.chaos.2019.05.014
Kumar, 2020, Existence of solutions of non-autonomous fractional differential equations with integral impulse condition, Adv. Differ. Eqs., 2020, 1
Jothimani, 2018, Existence result for a neutral fractional integro-differential equation with state dependent delay, J. Appl. Nonlinear Dyn., 7, 371, 10.5890/JAND.2018.12.005
Valliammal, 2018, Results on fractional neutral integro-differential systems with state-dependent delay in Banach spaces, Nonlinear Stud., 25
Panda, 2021, Results on system of Atangana-Baleanu fractional order Willis aneurysm and nonlinear singularly perturbed boundary value problems, Chaos Solitons Fract., 142, 110390, 10.1016/j.chaos.2020.110390
Nisar, 2021, An analysis of controllability results for nonlinear Hilfer neutral fractional derivatives with non-dense domain, Chaos Solitons Fract., 146, 110915, 10.1016/j.chaos.2021.110915
Ravichandran, 2019, New results on exact controllability of a class of fractional neutral integro-differential systems with state-dependent delay in Banach spaces, J. Franklin Inst., 356, 1535, 10.1016/j.jfranklin.2018.12.001
Kumar, 2020, New exact solitary wave solutions of the strain wave equation in microstructured solids via the generalized exponential rational function method, Eur. Phys. J. Plus, 135, 1, 10.1140/epjp/s13360-020-00883-x
Kumar, 2020, Lie symmetry analysis, exact analytical solutions and dynamics of solitons for (2+ 1)-dimensional NNV equations, Phys. Scr., 95, 095204, 10.1088/1402-4896/aba5ae
Kumar, 2019, Lie symmetry reductions and group invariant solutions of (2+ 1)-dimensional modified Veronese web equation, Nonlinear Dyn., 98, 1891, 10.1007/s11071-019-05294-x
Kumar, 2021, Some more closed-form invariant solutions and dynamical behavior of multiple solitons for the (2+ 1)-dimensional rdDym equation using the Lie symmetry approach, Res. Phys., 24, 104201
Ghanbari, 2021, The Lie symmetry analysis and exact Jacobi elliptic solutions for the Kawahara-KdV type equations, Res. Phys., 23, 104006
Ghanbari, 2020, Determining new soliton solutions for a generalized nonlinear evolution equation using an effective analytical method, Alexandr. Eng. J., 59, 3171, 10.1016/j.aej.2020.07.032
Munusamy, 2020, Existence of solutions for some functional integrodifferential equations with nonlocal conditions, Math. Methods Appl. Sci., 43, 10319, 10.1002/mma.6698
Ghanbari, 2020, Abundant solitary wave solutions to an extended nonlinear Schrödinger’s equation with conformable derivative using an efficient integration method, Adv. Differ. Eqs., 2020, 1
Vijayakumar, 2021, A new exploration on existence of Sobolev-type Hilfer fractional neutral integro-differential equations with infinite delay, Numer. Methods Partial Differ. Eqs., 37, 750, 10.1002/num.22550
Williams, 2020, A new study on existence and uniqueness of nonlocal fractional delay differential systems of order 1< r< 2 in Banach spaces, Numer. Methods Partial Differ. Eqs., 37, 949, 10.1002/num.22560
Dineshkumar, 2021, A discussion on the approximate controllability of Hilfer fractional neutral stochastic integro-differential systems, Chaos Solitons Fract., 142, 110472, 10.1016/j.chaos.2020.110472
M. Mohan Raja, V. Vijayakumar, R. Udhayakumar, K.S. Nisar, Results on existence and controllability results for fractional evolution inclusions of order 1< r< 2 with Clarke’s subdifferential type, Numer. Methods Partial Differ. Eqs. early view, in press
Raja, 2020, Results on the existence and controllability of fractional integro-differential system of order 1< r< 2 via measure of noncompactness, Chaos Solitons Fract., 139, 110299, 10.1016/j.chaos.2020.110299
Raja, 2020, A new approach on the approximate controllability of fractional differential evolution equations of order 1< r< 2 in Hilbert spaces, Chaos Solitons Fract., 141, 110310, 10.1016/j.chaos.2020.110310
He, 2020, A general numerical algorithm for nonlinear differential equations by the variational iteration method, Int. J. Numer. Methods Heat Fluid Flow, 30, 4797, 10.1108/HFF-01-2020-0029
Rani, 2020, Numerical inverse Laplace transform based on Bernoulli polynomials operational matrix for solving nonlinear differential equations, Res. Phys., 16, 102836
Odibat, 2020, An optimized decomposition method for nonlinear ordinary and partial differential equations, Physica A, 541, 123323, 10.1016/j.physa.2019.123323
Odibat, 2020, An improved optimal homotopy analysis algorithm for nonlinear differential equations, J. Math. Anal. Appl., 488, 124089, 10.1016/j.jmaa.2020.124089
Kurt, 2013, Fibonacci collocation method for solving linear differential-difference equations, Math. Comput. Appl., 18, 448
Kurt, 2013, Fibonacci collocation method for solving high-order linear Fredholm integro-differential-difference equations, Int. J. Math. Math. Sci., 2013, 10.1155/2013/486013
Mirzaee, 2014, Solving systems of linear Fredholm integro-differential equations with Fibonacci polynomials, Ain Shams Eng. J., 5, 271, 10.1016/j.asej.2013.09.002
Mirzaee, 2013, Solving singularly perturbed differential-difference equations arising in science and engineering with Fibonacci polynomials, Res. Phys., 3, 134
Mirzaee, 2017, A new collocation approach for solving systems of high-order linear Volterra integro-differential equations with variable coefficients, Appl. Math. Comput., 311, 272
H. Smith, An introduction to delay differential equations with applications to the life sciences, vol. 57, Springer Science & Business Media, New York, 2010.
T. Erneux, Applied delay differential equations, vol. 3, Springer Science & Business Media, New York, 2009.
Falcon, 2007, The k-Fibonacci sequence and the Pascal 2-triangle, Chaos Solitons Fract., 33, 38, 10.1016/j.chaos.2006.10.022
Falcon, 2009, On k-Fibonacci sequences and polynomials and their derivatives, Chaos Solitons Fract., 39, 1005, 10.1016/j.chaos.2007.03.007
Widatalla, 2012, Approximation algorithm for a system of pantograph equations, J. Appl. Math., 2012, 10.1155/2012/714681