RGNAA PublishingCommunications in Nonlinear Analysis2371-79209120210301On new fixed point results for some classes of enriched mappings in n-Banach spaces115132132ENEsraSimsekAtaturk UniversityIsaYildirimAtaturk University0000-0001-6165-716XJournal Article20210429We introduce the concepts of enriched n-contraction mapping, enriched n-Chatterjea mapping and enriched n-Kannan mapping in linear n-normed space. We prove some fixed point theorems for such mappings using Krasnoselsij iteration process in n-Banach spaces. The results presented in this paper improve the recent works of Berinde and Pacurar (J. Fixed Point Theory Appl. (2020) 22-38), Berinde and Pacurar (Preprint, arXiv:1909.03494) and Berinde and Pacurar (Preprint, arXiv:1909.02379, 2019) to linear n-normed spaces.RGNAA PublishingCommunications in Nonlinear Analysis2371-79209120210301Analytical Solution Of Fractional Order SIR Model Via Laplace Adomian Decomposition Method114138221ENAmjadAliGovt Post Graduate Jahanzeb College Saidu Sharif Swat, KP, PakistanMuradKhanGovt P.G Jahanzeb College Saidu Sharif Swat,KP, PakistanRahmatAli KhanMalakand University Chakdara, KP, PakistanJournal Article20200518In this article, we developed the scheme for approximate solutions of fractional order SIR model of infectious diseases. We obtain desert results in the form of infinite series with the Adomian decomposition method coupled with Laplace transform. In the last section of this work, we provide the numerical discussion for the proposed model and plots those results for illustrative purposes via Matlab.RGNAA PublishingCommunications in Nonlinear Analysis2371-79209120210301Generalized Monotone Method for System of Riemann-Liouville Fractional Reaction-Diffusion Equations120138225ENJagdish ANanwareShrikrishna Mahavidyalaya,Gunjoti0000-0002-3778-350XPandurang DKundgarDr.Babasaheb Ambedkar Marathwada University0000-0001-6827-5826Journal Article20210730In this paper, our aim is to obtain the integral representation for the solution of linear Riemann-Liouville reaction-diffusion equations of order $q$ in terms of Green's function where $ 0<q<1 .$ We have developed a generalized monotone method for non-linear weakly coupled system of Riemann-Liouville reaction-diffusion equations when the forcing term is the sum of increasing and decreasing functions. The generalized monotone method yields monotone sequences which converges uniformly and monotonically to coupled minimal and maximal solutions. Under uniqueness assumption, we proved the existence of a unique solution for the non-linear system of Riemann-Liouville reaction-diffusion equations.RGNAA PublishingCommunications in Nonlinear Analysis2371-79209120210301The Approximate Solution of COVID-19 Model by Variational Iteration Method118138226ENEiman.Department of Mathematics, University of Malakand, Chakdara Dir (Lower),
Khyber Pakhtunkhawa, Pakistan,HazratZamanUniversity of MalakandZakirUllahUniversity of MalakandJournal Article20210817In this work, we investigate a mathematical model of COVID-19 for approximate solution through variation iteration method (VIM). With the help of the said technique, we develop an algorithm to compute series type solution to the proposed problem. Then using some real values for the parameters and initial data, we compute few terms approximate solutions corresponding to different compartment. With the help of Mathematica, we also plot our approximate solutions for different compartment graphically.