An analytical study of Pythagorean fuzzy fractional wave equation using multivariate Pythagorean fuzzy fourier transform under generalized Hukuhara Caputo fractional differentiability

Agarval RP, Lakshmikantham V, Nieto J (2010) On the concept of solution for fractional differential equations with uncertainty. Nonlinear Anal Theory Methods Appl 72:2859–2862 Akram M, Ihsan T (2023) Solving Pythagorean fuzzy partial fractional diffusion model using the Laplace and Fourier transforms. Granular Comput 8:689–707 Akram M, Muhammad G (2023) Analysis of incommensurate multi-order fuzzy fractional differential equations under strongly generalized fuzzy Caputo’s differentiability. Granular Comput 8:809–825 Akram M, Muhammad G, Allahviranloo T (2019) Bipolar fuzzy linear system of equations. Comput Appl Math 38:1–29 Akram M, Saqib M, Bashir S, Allahviranloo T (2022) An efficient numerical method for solving \(m\)-polar fuzzy initial value problems. Comput Appl Math 41(4):157 Akram M, Yousuf M, Bilal M (2023) Solution method for fifth-order fuzzy initial value problem. Granular Comput. https://doi.org/10.1007/s41066-023-00403-z Akram M, Yousuf M, Allahviranloo T (2023) Solution of the Pythagorean fuzzy wave equation with Pythagorean fuzzy Fourier sine transform. Granular Comput. https://doi.org/10.1007/s41066-023-00400-2 Akram M, Muhammad G, Allahviranloo T, Ali G (2023) A solving method for two-dimensional homogeneous system of fuzzy fractional differential equations. AIMS Math 8(1):228–263 Akram M, Muhammad G, Ahmad D (2023) Analytical solution of the Atangana–Baleanu–Caputo fractional differential equations using Pythagorean fuzzy sets. Granular Comput 8:667–687 Akram M, Ihsan T, Allahviranoloo T (2023) Solving Pythagorean fuzzy fractional differential equations using Laplace transform. Granular Comput 8(3):551–575 Allahviranloo T (2006) Difference methods for fuzzy partial differential equations. Comput Methods Appl Math 2(3):233–242 Allahviranloo T, Afshar KM (2010) Numerical methods for fuzzy linear partial differential equations under new definition for derivative. Iran J Fuzzy Syst 7(3):33–50 Allahviranloo T, Ahmadi MB (2010) Fuzzy Laplace transforms. Soft Comput 14:235–243 Allahviranloo T, Armand A, Gouyandeh Z (2014) Fuzzy fractional differential equations under generalized fuzzy Caputo derivative. J Intell Fuzzy Syst 26:1481–1490 Allahviranloo T, Ghobadi M, Matinfar M (2020) A fuzzy solution of wave equation by FFS-transform. Numer Methods Partial Differ Equ. https://doi.org/10.1002/num.22661 Atanassov KT (1983) Intuitionistic fuzzy sets. In: VII ITKR’s session, Sofia (Deposed in central science-technical library of Bulgarian Academy of Science, 1697/84) (in Bulgarian) Bayrak MA (2013) Approximate solution of wave equation using fuzzy number. Int J Comput Appl 68:975 Bede B, Gal SG (2005) Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy ordinary differential equations. Fuzzy Sets Syst 151(3):581–599 Bede B, Stefanini L (2013) Generalized differentiability of fuzzy-valued functions. Fuzzy Sets Syst 230:119–141 Bede B, Lovane G, Esposito I (2005) Fuzzy Fourier transforms and their application to fingerprint identification. J Discrete Math Sci Cryptogr 8(1):59–79 Bertone AM, Jafelice RM, de Barros LC, Bassanezi RC (2013) On fuzzy solution for partial differential equations. Fuzzy Sets Syst 219:68–80 Buckley JJ, Feuring T (1999) Introduction to fuzzy partial differential equations. Fuzzy Sets Syst 105:241–248 Chang SS, Zadeh LA (1972) On fuzzy mapping and control. IEEE Trans Syst Man Cybern SMC–2:30–34 Chen SJ, Chen SM (2001) A new method to measure the similarity between fuzzy numbers. In: Proceedings of the 10th IEEE international conference on fuzzy systems, proceedings of the 8th international fuzzy systems, integration, Melbourne, Australia Chen SM, Fang YD (2005) A new method to deal with fuzzy classification problems by tuning membership functions for fuzzy classification systems. J Chin Inst Eng 28(1):169–173 Chen SM, Jian WS (2017) Fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups, similarity measures and PSO techniques. Inf Sci 391–392:65–79 Chen SM, Lin HL (2005) Generating weighted fuzzy rules for handling classification problems. Int J Electron Bus Manag 3(2):116–128 Chen SM, Niou SJ (2011) Fuzzy multiple attributes group decision-making based on fuzzy preference relations. Expert Syst Appl 38(4):3865–3872 Chen SM, Phuong BDH (2017) Fuzzy time series forecasting based on optimal partitions of intervals and optimal weighting vectors. Knowl Based Syst 118:204–216 Chen SM, Wang NY (2010) Fuzzy forecasting based on fuzzy-trend logical relationship groups. IEEE Trans Syst Man Cybern Part B (Cybern) 40(5):1343–1358 Chen YY, Chang YT, Chen BS (2009) Fuzzy solution to partial differential equations: adoptive approach. IEEE Trans Fuzzy Syst 17:116–127 Chen SM, Ko YK, Chang YC, Pan JS (2009) Weighted fuzzy interpolative reasoning based on weighted increment transformation and weighted ratio transformation techniques. IEEE Trans Fuzzy Syst 17(6):14121–1427 Dubois D, Prade H (1978) Operations on fuzzy numbers. Int J Syst Sci 9:613–626 Ezadi S, Allahviranloo T (1972) Artificial neural network approach for solving fuzzy fractional order initial value problems under gH-differentiability. Math Methods Appl Sci. https://doi.org/10.1002/mma.7287 Gouyandeh Z, Allahviranloo T, Abbasbandy S, Armand A (2017) A fuzzy solution of heat equation under generalized Hukuhara differentiability by fuzzy Fourier transform. Fuzzy Sets Syst 309:81–97 Kaleva O (1987) Fuzzy differential equations. Fuzzy Sets Syst 24:301–317 Kilbaz AA, Srivastava HM, Trujillo JJ (2006) Theory and applications of fractional differential equations, vol 204. Elsevier, London, pp 1–523 Lmutairi M, Zureigat H, Ismail AI, Jameel AF (2021) Fuzzy numerical solution via finite difference scheme of wave equation in double parametrical fuzzy number form. Mathematics 2021:9667 Long HV, Son NTK, Tam HTT (2017) The solvability of fuzzy fractional partial differential equations under Caputo gH-differentiability. Fuzzy Sets Syst 309:35–63 Luqman A, Akram M, Alcantud JCR (2020) Digraph and matrix approach for risk evaluations under Pythagorean fuzzy information. Expert Syst Appl 170:114–518 Melliani S, Elomari M, Hilal K, Menchih M (2021) Fuzzy fractional differential wave equation. J Optim Theory Appl 1(2):42 Oberguggenbberger M (2004) Fuzzy and weak solution to differential equations. In: Proceedings of the 10th international IPMU conference, pp 517–524 Podlubny I (1998) Fractional differential equations: an introduction to fuzzy derivatives, fractional differential equations, to methods of their solutions and some of their applications, vol 198. Elsevier, London, pp 62–86 Puri ML, Ralescu DA (1983) Differentials of fuzzy functions. J Math Anal Appl 91:552–558 Salahshour S, Allahviranloo T (2013) Application of fuzzy Laplace transforms. Soft Comput 17:145–158 Salahshour S, Allahviranloo T, Abbasbandy S (2012) Solving fuzzy fractional equations by fuzzy Laplace transforms. Commun Nonlinear Sci Numer Simul 2012:1372–1381 Seikkala S (1987) On the fuzzy initial value problem. Fuzzy Sets Syst 24:319–330 Shen VR, Chung YF, Chen SM, Guo JY (2013) A novel reduction approach for Petri net systems based on matching theory. Expert Syst Appl 40(11):4562–4576 Stefanini L (2010) A generalization of Hukuhara difference and division for interval and fuzzy arithmetic. Fuzzy Sets Syst 161:1564–1584 Stefanini L, Bede B (2009) Generalized Hukuhara differentiability of fuzzy-number-valued functions with interval differential equations. Nonlinear Anal 71:1311–1328 Vu H, Hoa NV (2019) Uncertain fractional differential equations on a time scale under granular differentiability concept. Comput Appl Math 38:1–22 Yager RR (2013) Pythagorean fuzzy subsets. In: 2013 joint IFSA world congress and NAFIPS annual meeting, pp 57–61 Yager RR (2014) Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst 22:958–965 Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353 Zhang X, Xu Z (2014) Extension of TOPSIS to multiple criteria decision-making with Pythagorean fuzzy sets. Int J Intell Syst 29(12):1061–1078